This thesis describes the results of computer simulations of cosmic ray extensive air showers with primary energy in the range 10 (^14) – 10 (^19) eV. A brief review of simulations made by other authors is presented after which models for high energy nuclear interactions are discussed. The parameters chosen for the preferred model employed here are stated and some more recent data from accelerator experiments are mentioned. The predictions from the preferred model for proton initiated air showers are compared with experimental data and the results of previous simulations; the consequences of including trends seen from recent accelerator experiments in the model for interactions are also discussed. The break-up of energetic particles with atomic mass number as high as 56 as they traverse the atmosphere is discussed and a model to reconstruct this process at cosmic ray energies is described. The predictions from the preferred model for interactions assuming iron primary particles are given. It is concluded that a study of the average shower characteristics will not lead to a reliable determination of the mass composition of the primary radiation. Predictions for the fluctuations of measurable parameters in air showers are presented; it is shown that on the basis of these studies it is likely that comment may be made upon the primary composition. The results of these simulations are particularly relevant to the Haverah Park Extensive Air Shower Array; the improvements to the array presently being implemented should, according to the present results, enable an estimation of the primary composition IV at energies > 10 (^17) eV to be made. In particular the presence or otherwise of protons in the primary beam should be estimated. The feasibility of the cluster analysis of experimental data is investigated and it is shown on the basis of the clustering of simulation data that to a limited extent the separation of air showers into groups according to the atomic mass number of the primary particle is possible