The differential scattering characteristics of closed three-dimensional dielectric objects are theoretically investigated. The scattering problem is solved in a spherical basis by the Extended Boundary Condition Method (EBCM) which results in a system of linear equations for the expansion coefficients of the scattered field in terms of the incident field coefficients. The equations are solved numerically for dielectric spheres, spheroids, and finite cylinders to study the dependence of the differential scattering on the size, shape, and index of refraction of the scattering object. The method developed here appears to be most applicable to objects whose physical size is on the order of the wavelength of the incident radiation.