A fast and simple method for direct electromagnetic scattering problems related to multilayer cylindrical objects having arbitrary shaped dielectric or conducting layers is presented. First, the field in each layer is represented as a series of Bessel and Hankel functions with unknown coefficients. Then, the continuity of the field, along with its radial derivative, is imposed and two equations for several unknowns are obtained for each boundary. By taking the inner products of these equations with complex exponential functions and using the orthogonality property, the equations are augmented to form a linear system for relatively small number of unknown coefficients that can easily be solved. Once these coefficients are determined, one can compute the field value anywhere including the inner regions of the multilayer structure. It has been numerically shown that, for multilayer objects having homogeneous layers and piecewise smooth boundaries, the proposed method is a significantly simple and fast alternative to general purpose numerical techniques.