Abstract: The theory of plastic deformation in the impact of cylindrical projectiles on rigid targets was first introduced by G. I. Taylor(1948)^[1]. The importance of this theory lies in the fact that the dynamic yield strength of the materials can be determined from the measurement of the plastic deformation of flat-ended cylindrical projectiles. From the experimental results^[2] we find that the dynamic yield strength is independent of impact velocity, and that it is higher than the static yield strength in general, and several times higher than the static yield strength in certain cases. This gives an important foundation for the study of elastoplastic impact problems in general. However, it is well known that the complexity of differential equations in Taylor's theory compelled us to use the troublesome numerical solution. In this paper, the analytical solution of all the equations in Taylor's theory is given in parametrical form and the results are discussed in detail.In the latter part of this paper, the method of calculation of impulse of impact is improved by considering the processes of radial' movement of materials. The analytical solution of the improved theory shows that it gives better agreement with the experimental results than that of original Taylor's theory.