The main purpose of this thesis is to investigate, from a modeling point of view, the migration of GRINDSTEDr SOFT-N-SAFE (SNS) and other plasticisers from polyvinyl chloride (PVC) and polyolefin food package materials and into foodstuff (specifically the four food simulants set by EU legislation). In this work it is shown how diffusion coefficients can be obtained by regression of experimental migration data plotted as the square root of time. This was done from plasticiser migration data of GRINDSTEDr SOFT-N-SAFE, GRINDSTEDr ACETEM 95 CO (Acetem) and Epoxidised Soybean Oil (ESBO) migrating from Polyvinyl Chloride (PVC) and into iso-octane at 20◦C, 40◦C and 60◦C. Using these experimentally obtained diffusion coefficients the migration was modeled using two analytical models with relatively good accuracy. The diffusion coefficient in highly plasticised PVC should, however, not be considered uniform over the whole polymer layer when the migrant is the plasticiser itself. It was attempted to predict the diffusion coefficient of SNS in highly plasticised PVC from pure component data alone, using the model by Vrentas and Vrentas, which is based on the free volume theory. The results, however, showed that the model under-predicts the experimental diffusion coefficient values. These experimentally obtained values should be regarded as average diffusion coefficient values of the whole polymer and lower than the diffusion coefficient of the fully plasticised PVC. Instead of using this elaborated complex model, it was decided to use the much simpler semi-empirical model by Piringer. Using this simple model, with a polymer-specific parameter obtained from ESBO migration data alone, it was possible to estimate diffusion coefficients for Acetem and SNS. The results were close to the experimentally obtained diffusion coefficients at 20◦C, except at higher temperatures. Using the finite element mesh method in Matlab and COMSOL environments the migration was modeled with a diffusion coefficient able to change with local plasticiser concentration. Three different models for this plasticiser concentration dependence of the diffusion coefficient were evaluated. All models performed similarly, with better predicting ability compared to modeling with a static diffusion coefficient. This numerical solution by the finite element mesh method has also been used to model the migration of an antistatic additive to the surface of Low Density Polyethylene (LDPE) and Poly Propylene (PP). It was possible with a newly developed model to estimate the migration with very high accuracy. This result leads to the somewhat surprising conclusion that the controlling step in the migration of the additive to the surface was not the migration within the polymer bulk. Migration is probably due to a temperature dependent partitioning of the additive between the polymer bulk and the surface layer. The possibility of using molecular dynamics calculations to estimate the partition coefficients of additives between polymers and foodstuff was also investigated. The development of the methodology was done against experimental data of a system composed of a hydrophilic or a hydrophobic additive between LDPE and different ethanol/water mixtures. The calculated partition coefficients of different additives between LDPE and ethanol/water were correlated with high accuracy against experimental data. To extend the methodology to acetic acid systems (food simulant B), it was chosen firstly to investigate the predictive capabilities of the TraPPE, OPLS-AA and CHARMM27 force fields for pure acetic acid and acetic acid / water mixtures. None of the three force fields was able to predict satisfactorily the density of acetic acid / water mixtures. Only the CHARMM27 force field was able to predict the local density maxima of the system. A hydrogen bond connectivity counting code was developed for investigating the clustering of acetic acid. Statistics using the cluster counting code showed that the acetic acid molecules in the liquid phase mostly formed chain-like structures, with chains of 2 and 3 molecules in size to be the most predominant ones. Furthermore, the ability of the force fields to predict the enthalpy of vaporization was tested. All three force fields over-predict this property, resulting to a value about twice the experimental one ( 50kJ/mol compared to 23.7kJ/mol). The gas phase consisted almost entirely of monomers, where experimental Pressure-Volume data of the gas phase at 298K and 1 bar give a dimer fraction of around 80-90%. This dimer fraction in the gas phase was elevated using higher atomic charges as shown by Chocholousova et al.[J. Chocholousova, J. Vacek, and P. Hobza; J. Phys. Chem. A; 107, 17, (2003), 3086-3092], but the calculated enthalpy of vaporization was still almost twice as high. It was shown that most literature data listing a value of 50kJ/mol originate from the work by Konicek and Wads¨o[J. Konicek and I. Wads¨o; Acta Chem. Scand.; 24, 7, (1970), 2612-2616] from 1970. In the same work is explained how the enthalpy of vaporization of acetic acid theoretically can be seen as consisting of two contributions, the ”pure” enthalpy of vaporization of the monomer and the enthalpy of dissociation. It is important that this theoretically-derived ”pure”enthalpy of vaporization (which is 50kJ/mol) is not confused with the experimentally obtained enthalpy of vaporization (23.7kJ/mol). The OPLS-AA force field is parameterized towards the theoretical ”pure” enthalpy of vaporization in a correct way, by only calculating the energy difference for the single acetic acid monomer molecule between the two phases. However simulations in this work have shown that these parameters do not allow the force field to predict the gas phase dimer fraction accurately. Overall from this work it can be concluded that a full prediction of migration in polyolefins can be obtained using the numerical solution by finite element mesh together with diffusion coefficients obtained from the Piringer model and partition coefficient by molecular dynamics. For the complex system of migration of plasticisers in highly plasticised PVC, a full predicitive model was not obtained. A model was, however, developed for this system that predicts satisfactorily with only 1 or 2 adjustable parameters to plasticiser migration from PVC.