Where closely jointed rock masses are encountered in slopes, failure can occur both through the rock mass, as a result of combination of macro and micro jointing, and through the rock substance. Determination of the strength of the category of rock mass is extraordinarily difficult since the size of representative specimens is too large for laboratory testing. This difficulty can be overcome by using a non-linear rock mass failure criterion or by back analysis of such slopes to estimate the rock mass strength. In this paper, a practical procedure and a computer program are presented for the back determination of shear strength parameters mobilized in slopes cut in closely jointed rock masses which obey a non-linear failure criterion rather than a linear one. The procedure shows that the constants to derive normal stress dependent shear strength parameters of the failed rock masses can be determined by utilizing a main cross-section and without a pre-determined value of rock mass rating (RMR). Trials are made for different RMRm and RMRs values corresponding to various possible combinations of the constant m and s, which are used in the Hoek-Brown failure criterion, satisfying the limit equilibrium condition. It is also noted that the procedure provides a quick check for the rock mass rating obtained from the site investigations. The method is used in conjunction with the Bishop's method of analysis based on circular slip surfaces. The procedure outlined in this paper has also been satisfactorily applied to documented slope failure case histories in three open pit mines in Turkey. (C) 1998 Elsevier Science Ltd.