In this report, we present the method of integral transforms and the Gauss-Chebyshev quadrature methods to solve the problem of a crack parallel to a rigid boundary under remote tension. We derive a system of singular integral equations of the first kind, specific to the problem at hand, which we numerically solve using Gauss-Chebyshev integration. We specialize our results to the problem of a crack in an infinite plate under remote tension, and show that the relative error in our numerically derived solutions are within machine precision of the closed-form analytical solutions. Stress intensity factors are calculated that are in excellent agreement with those derived by others using different methods. We also demonstrate that both the stress intensity factors and normal sigma sub yy x, y and shear sigma sub xy x, y stress fields derived via numerical solution of the singular integral equations, compare well with those determined using the commercially available Abaqus finite element code where the crack is modeled using the eXtended Finite Element Method.