This paper formulates an empirical strength criterion for the heterogeneous Antalya tufa rock mass assuming that the heterogeneity effect is represented by the unit weight and the porosity of the tufa rock, which is highly variable from a geomechanical point of view. Unconstrained non-linear regression analyses have been used to identify the strength criterion and material constants in terms of fitting an equation and determining its regression parameters. Prior to this approach, the fitting of the laboratory data to the failure criteria defined by Coulomb (Mem Acad R Des Sci 3:38, 1776), Bieniawski (J S Afr Inst Min Metal 74(8):312-320, 1974) and Hoek and Brown (J Geotech Eng Div ASCE 106(GT9):1013-1035, 1980) has been performed by means of constrained regression analyses. For the regression analyses, the results of the uniaxial and triaxial compressive strength tests along with the Brazilian tensile strength tests have been used. The regression analysis has been performed in two stages. In the first stage, the results of the uniaxial and triaxial compressive strength tests have been included in the analyses; in the second stage, the results of the Brazilian tensile strength tests have been added to the regression analyses performed in the first stage.