This paper describes a numerical technique for modeling large numbers of circular inclusions, circular holes, and straight cracks in an infinite elastic solid. The analysis is based on a complex hypersingular integral equation that is written directly in terms of the displacement discontinuities and tractions at the boundaries. The tractions along the boundaries of the inclusions and the displacements along the boundaries of the holes are represented by truncated complex Fourier series, and series of Chebyshev polynomials are used to approximate the displacement discontinuity distributions along the cracks. A Galerkin (weighted residual) procedure is adopted to develop the system of simultaneous linear algebraic equations for the overall problem, and a Gauss-Scidel algorithm is used to solve this system. Two numerical examples are given to demonstrate the effectiveness of this approach.