The objective of this study is to investigate the physical and mechanical properties of steel fiber-reinforced concrete under compression, including: modulus of elasticity, Poisson's ratio, ultimate compressive strain values, and compressive strength with varying percentages of randomly distributed fiber reinforcement. An experimental program was developed and executed, which included the fabrication of cube specimens with dimensions of 100 × 100 × 100 mm, and compressive testing under static loading conditions, incorporating unloading from the inelastic deformation range. Two types of steel fibers were selected for the random reinforcement: anchored and corrugated profiles. The volumetric content of steel fiber in the cube specimens was 0.5%, 1.0%, 1.5%, and 2.0%. The experimental investigations yielded strength and deformation characteristics of steel fiber-reinforced concrete under compression. Based on the experimental data, true stress-strain diagrams for steel fiber-reinforced concrete were constructed, considering the type and volumetric percentage of the reinforcing fibers. A constitutive law for steel fiber-reinforced concrete, based on the obtained diagrams, is proposed, which can be described by a fourth-degree polynomial function with constant coefficients defining the shape of the stress-strain curve. The presented research findings can be utilized in the development of a methodology for physically nonlinear analysis of steel fiber-reinforced concrete elements with a randomly distributed fiber reinforcement percentage ranging from 0.5% to 2.0%. The proposed constitutive law provides a valuable tool for engineers to accurately model the nonlinear behavior of steel fiber-reinforced concrete elements in physically nonlinear analyses, leading to safer and more efficient designs.