Abstract This paper deals with the in-plane dynamic modeling of generally shaped arches with a varying cross-section in undamaged or damaged configuration, under different boundary conditions and external forces. The Generalized Differential Quadrature (GDQ) method is herein applied to solve numerically the problem without passing through any variational formulation, but solving directly the governing equations of motion in strong form. The main purpose of the work is to obtain a computationally efficient higher-order method for solving time integration problems. The total time interval is discretized in time steps and the GDQ method is applied to solve the initial value problem within each time step. At each time interval, a linear algebraic equation system has to be solved. A simple and efficient implementation scheme is presented. A wide GDQ-based numerical investigation is performed to study the linear dynamics of the arch with different geometries, boundary conditions and external forces. The numerical results based on the application of the GDQ method are compared with those ones provided by the Newmark method. A very good agreement is found between the two numerical approaches, which demonstrates the performance and feasibility of the proposed GDQ-time-stepping algorithm for transient dynamics.