In analyzing the crack problems under the contact loading condition, the pressure distribution on the contact region is usually assumed to be distributed elliptically. However, the existence of the cracks may require some modifications of the well-known Hertz's theory which expresses the relationship between the distribution of the contact pressure, the contact width, the total load of the indentation and the radius of curvature of the indenter. In this paper, a computational method for the cracks in a half-plane under the contact loading condition is developed with consideration to effect of the cracks on the contact pressure distribution. In this method, the continuous dislocations model is employed. From the results of the numerical calculations, it is concluded that when the crack is not small and is located near the contact area, Hertz's theory does not give a sufficiently accurate contact pressure distribution.Presented as a Society of Tribologists and Lubrication Engineers paper at the STLE/ASME Tribology Conference in St. Louis, Missouri, October 14–16, 1991