Computational studies have been used in conjunction with theoretical approaches to investigate a number of problems in stellar dynamics. These problems have particular relevance to globular star clusters. The investigations began in the area of three-body scattering (i.e. encounters between a binary and a single star), dealing especially with close triple encounters. A prediction was made, using two theoretical approaches, of the probability distribution for the energy of the binary at the end of an encounter, in cases where the energy is either very large or very small. Programs were written to run on the Edinburgh University mainframe computer to provide a numerical test of the theory. To tackle larger problems an N-body code has been developed for the Edinburgh Concurrent Supercomputer, and its performance analysed. The analysis included a brief study of the optimum order of the algorithm used for this code. The program has been used to simulate Plummer model star clusters containing 1024 and 10048 stars. From the results of these simulations, investigations have been made into the problems of Lagrangian radii oscillations and core wandering. The latter is the motion of the densest part of the star cluster, whilst the former is to do with the movement of mass towards and away from this position. The approach involved a direct look at the variation in the coordinates, supplemented by the computations of autocorrelations and variances.