The subject of this dissertation is the analysis and solution of the equations describing the laminar boundary layer on axisymmetric bodies immersed in an oncoming stream and spinning at a constant rate about their axis of revolution. The flow is allowed to be compressible or incompressible and the geometries for which solutions are obtained include the sphere, cone, paraboloid, hyperboloid and tangent ogive. The only limitation on spin rate involves the assumption that the pressure across the boundary layer remain essentially constant. The method of solution for the set of parabolic nonlinear partial differential equations which describe the boundary layer is an implicit finite difference technique. A study of step size and convergence criteria is included to determine the accuracy of the numerical method. Comparisons with previous approximate methods are also presented in an effort to establish confidence in these results. Boundary layer characteristics in the form of shear stress, heat transfer, velocity and temperature profiles, displacement thickness and frictional drag and moment coefficients are presented for each geometry over a wide range of spin rates. / Ph. D.