The histories and distributions of dynamic stresses in an orthotropic hollow cylinder under sinusoidal impact load are obtained by making use of eigenfunction expansion method in this paper. Dynamic equations for axially symmetric orthotropic problem are founded and results are carried out for a practical example in which an orthotropic hollow cylinder is in initially at rest and subjected to a dynamic interior pressure $p(t)=-{sigma}_0(sin{alpha}t+1)$. The features of the solution appear the propagation of the cylindrical waves. The other hand, a dynamic finite element solution for the same problem is also got by making use of structural software (ABAQUS) program. Comparing theoretical solution with finite element solution, it can be found that two kinds of results obtained by two different solving methods are suitably approached. Thus, it is further concluded that the method and computing process of the theoretical solution are effective and accurate.