We consider a general solution of the electromagnetic wave scattering problem for arbitrarily shaped homogeneous particles, whose surface can be expressed by a function of angular coordinates, using a Laplace series expansion. This can include regularly shaped particles (e.g., ellipsoids and cubes) as well as irregularly shaped particles like Gaussian spheres. For calculations of scattering properties of the particles, we use the approach based on the Sh-matrix. The Sh-matrix elements deduced from the T-matrix technique allow one to separate the shape effects from sizeand refractiveindex-dependent parameters. The separation also allows the corresponding surface integrals to be solved analytically for different particle shapes. In this manuscript, we give analytical expressions for the Sh-matrix elements for arbitrary shaped particles that can be presented with Laplace series. We find good agreement between results obtained comparing our and DDA calculations. Published by Elsevier Ltd.