Polymer electrolytes are widely used as ion transport media in vital applications such as energy storage devices and electrochemical displays. To further develop these materials, it is important to understand their ionic conductivity mechanisms. It has long been thought that ionic conduction in a polymer electrolyte occurs in the amorphous phase, while the crystalline phase is insulating. However, this picture has recently been challenged by the discovery of the crystalline system LiXF6∙PEO6 (X=P, As or Sb) which exhibits higher conductivity than its amorphous counterpart. Their structures comprise interlocking hemi-helical PEO-chain pairs containing Li+ ions and separating them from the XF6- anions. The first Molecular Dynamics (MD) simulation study of the LiPF6∙PEO6 system is presented in this thesis. Although its conductivity is too low for most applications at ambient temperature, it can be enhanced by iso- and aliovalent anion doping. It is shown that the diffraction-determined structure is well reproduced on simulating the system using an infinite PEO-chain model. The Li-Oet coordination number here becomes 6 instead of 5; minor changes also occur in the polymer backbone configuration. The crystallographic asymmetric unit and diffraction profiles are also reproduced. On simulating a shorter-chain system (n=22), more resembling the real material, the structure retains its double hemi-helices, but the polymer adopts a more relaxed conformation, facilitating the formation of Li+-PF6- pairs. Infinite-chain simulation shows the ionic conduction to be dominated by anion motion, in contrast to earlier NMR results. The effects of doping are also reproduced. Shortening the polymer chain-length has the effect of raising the transport number for lithium, thereby bring it into better agreement with experiment. It can be concluded that it is critical to take polymer chain-length and chain-termination into account when modelling ionic conductivity mechanisms in crystalline polymer electrolytes.