The axial vibration problem formulation and solution of a inhomogeneous rod modeled as a continuous system were analyzed. The solutions are obtained in the Laplace space and the inverse transformation into the real time domain is performed using Residue theorem. Their efficiency is demonstrated by comparing the results with those obtained using Mode Superposition Method. The results are presented in the form of graphs for load type. The inhomogenity parameter used in inhomogeneous models is found to be effective in the response of the rod.