This paper provides a systematic approach to solve in-plane free vibrations of arches with variable curvature. The proposed approach basically introduces the concept of dynamic stiffness matrix into a series solution for in-plane vibrations of arches with variable curvature. An arch is decomposed into as many elements as needed for accuracy of solution. In each element, a series solution is formulated in terms of polynomials, the coefficients of which are related to each other through recurrence formulas. As a result, in order to have an accurate solution, one does not need a lot of terms in series solution and in Taylor expansion series for the variable coefficients of the governing equations due to the consideration of variable curvature. Finally, a dynamic stiffness matrix is formed such that it can be applied to solve more complicated systems such as multiple-span arches. In the whole analysis, the effects of rotary inertia and shear deformation have been taken into account.