Free vibration of symmetric angle-ply layered conical shell frusta of variable thickness is analyzed under shear deformation theory with different boundary conditions by applying collocation with spline approximation. Linear and exponential variation in thickness of layers are assumed in axial direction. Displacements and rotational functions are approximated by Bickley-type splines of order three and obtained a generalized eigenvalue problem. This problem is solved numerically for an eigenfrequency parameter and an associated eigenvector of spline coefficients. The vibration of three and five-layered conical shells, made up of two different type of materials are considered. Parametric studies are made for analysing the frequencies of the shell with respect to the coefficients of thickness variations, length-to-radius ratio, length-to-thickness ratio and ply angles with different combination of the materials. The results are compared with the available data and new results are presented in terms of tables and graphs.