The purpose of this paper is to present details of an algorithm for performing the numerical analysis of in-plane free vibration problem of curved beam by using the finite element technique. Although the finite element techniques for the straight or flat structures such as rods, beams and plates are well established, the finite element formulation for curved beam has not yet been completely discussed because of analytical complexity of the beam. The analysis of curved beam is reduced to the coupled problems of the axial and the transverse components of forces, bending moments, displacements and slopes in the beam. Sabir and Ashwell have discussed the vibrations of a ring by using the shape functions (interpolation functions) based on simple strain functions. The discrete element displacement method was applied to the vibrations of shallow curved beam by Dawe. Suzuki et al have presented the power series expansions method for solving free vibration of curved beams. Irie et al have used spline functions to analyse the in-plane vibration of the varying cross section beams supported at one end.