The problem of crack initiation and growth in contact problems is studied by the strain energy density theory. This is accomplished by considering each point of the body as a possible source of crack initiation. The direction of crack initiation is determined by calculating the minimum value of the strain energy density function along a circular core area surrounding the point. The crack initiates from the point with the maximum of the local minimum values of the strain energy density function. Considered is a circular disc subjected to two equal and opposite forces and a circular cylindrical body pressed by a cylindrical punch. The stress field for the first case is obtained from the classical elasticity solution, while a finite element code is used for the second case. The locations of fracture initiation and the subsequent fracture trajectories for fast unstable fracture are determined.