The problem of an elastic half plane loaded in tension and weakened by a rectangular trench is set up in a manner leading to a system of simultaneous singular integral equations. The method is to consider the superposition of solutions for two cracks perpendicular and one parallel to the surface of the half plane. The limiting case when the three cracks intersect appropriately leads to the geometry of a rectangular trench. A collocation scheme developed by Erdogan and Gupta leads to numerical solution of the equations to determine the stress intensity factors at the corners and the horizontal displacement of the trench wall.