The first part of the present paper is devoted to the analysis of the standard Brazilian test, based on the theory of elasticity. Some literature data on the differences between the tensile strength Sr in the usual sense and the approximate strength Srb are quoted for some types of French rocks. The results of the present author's experimental studies of three types of Polish rocks are discussed, the causes of the differences between Sr and Srb being analysed. In the second part of the paper it is proposed to consider the Brazilian test as a problem of the theory of limit states, showing that the assumption of a modified Coulomb condition is in agreement with the mode of the fracture of the test specimen used. lt is found that such a method leads to quite realistic approximate values of the tensile strength.