In this study, time response of a planar curved beam with variable curvatures under in-plane impact load is analyzed by two numerical methods which are Finite Difference and Finite Element Methods. The solution procedures in both methods are based on solution of eigenvalue and time response problems. Catenary form is selected as the axis of curved beam. A computer program is developed in Mathematica for the solution with Finite Difference Method. Moreover, a computer code is written for the geometric and finite element models of curved beam with variable curvature in ANSYS by using APDL (ANSYS Parametric Design Language). Solutions of the two methods are compared in each other and then good agreement is observed. The effects of impuls and damping properties on the time response are investigated.