The integral equation relating displacement gradient along the free surface of an elastic half-space containing a vertical strike-slip fault to the stress on the fault faces is developed. An estimate of fault friction stress and fault depth is obtained by approximating the fault stress as a smooth polynomial with unknown coefficients. Values of these coefficients are then obtained by matching the theoretically predicted surface displacements with measured data and by requiring the stresses ahead of the fault to be nonsingular. The choice of a quadratic polynomial (two unknown coefficients) is sufficient to produce good matching of predicted and measured surface displacements and to predict reasonable fault stress variation and fault depth. The calculations indicate that meaningful results may be obtained without demanding high precision in the measured surface displacement data.