<p>This study presents a methodology for fitting the uniaxial compressive strength (UCS) and tensile strength (TS) of rocks and concrete material, using the nonlinear failure criterion proposed by Úcar. A selected of triaxial test data was compiled from the literature and systematically filtered to retain only data consistent with the brittle failure behaviour. For each lithology, the relationship between the principal stresses was modelled through nonlinear regression, allowing estimation of the UCS and TS parameters. These were used to calculate and adjust ξ = TS/UCS, parameter of the Úcar failure criterion, quantifying the variation using the Taylor series expansion. Failure envelopes models are proposed for the six rock types analyzed as well as for the concrete. A comparative case study based on Coburg limestone, using the proposed regression methodology of the Úcar criterion versus the Hoek and Brown criterion against Bayesian and heuristic alternatives, yielded successful results. A key advantage of the Úcar criterion is that it requires only UCS and TS as input parameters. The proposed methodology is especially valuable during the early stages of geotechnical and rock engineering projects, or under budget limitations, where experimental datasets are often sparse or unavailable. In addition, the general rock-type models developed herein enable strength prediction for intact rock in contexts where only lithology is known or available data are limited.</p>