Abstract When the effects of both the shear deformation and rotary inertia are considered, the literature regarding the free vibration analysis of circular arches using the finite arch elements is rare. To the authors’ knowledge, Int. J. Numer. Methods Eng. 52 (2001) 273–286 is the latest work of the literature that deals with this in detail. Since the procedures for deriving the stiffness and mass matrices of the arch element are tedious and complicated in available literature, this paper tries to present a simple approach to overcome these drawbacks. First, the three functions for the radial (or normal), tangential and rotational displacements of an arch element are assumed. Since each function consists of six integration constants, one has 18 unknown constants for the three displacement functions. Next, from the last three displacement functions, the three force–displacement differential equations and the three static equilibrium equations for the arch element, one obtains three polynomial expressions. Equating to zero the coefficients of the terms in each of the last three expressions, respectively, one obtains 18 equations as functions of the 18 unknown constants. Excluding the 6 dependent ones among the last 18 equations, one obtains 12 independent equations. Solving for the last 12 independent equations yielded a unique solution in terms of six unknown constants. Finally, imposing the boundary conditions at the two ends of an arch element determines the last six unknown constants and completely defines the three displacement functions. By means of the displacement functions, one may calculate the stiffness and mass matrices of each arch element and then perform the free vibration analysis of the arches. Good agreement between the results of this paper and those of the existing literature validated the presented approach.