This paper presents a numerical method of evaluating view factors between planar surfaces which is computationally efficient and quite general to program on a computer. The method, which is based on Gaussian quadrature to perform the contour integration is extended to surfaces with curved boundaries. The performance of various quadrature formulas viz. trapezoidal, Simpson and Gaussian, have been compared for performance by applying them to sample problems. The Gaussian quadrature method with nonlinear transformation to map the boundary has been found to be the most accurate, computationally faster and very general. As an application, the shape factor between two elliptic surfaces has been evaluated.