Horizontal subsurface cracks in an elastic-plastic material are analysed using finite-element techniques. The sliding surface is modelled as a rigid cylinder. The effect of such parameters as the friction between the cylinder and the material being indented, the elastic and plastic modulus of the material and the depth of crack location on the J-integral values at the left and right tips of a horizontal subsurface crack is considered. The prospective crack propagation direction is taken as the direction along which the J integral assumes a maximum as the indenter slides along the material surface. The left and right tip cracks were found likely to propagate at about 10 degrees to the horizontal. This propagation direction was found to depend strongly on the location of the crack. Both crack tips are expected to propagate closer to the vertical direction as the depth of crack location is reduced. Also, horizontal cracks closer to the surface are found to have higher J integral values. While friction between the slider and the specimen did not affect the crack propagation direction, the crack-tip plasticity reduced the propagation direction, with respect to the horizontal.