Quaternary compounds are highly desirable for realizing advanced optoelectronic and spintronic devices. We have systematically studied the effects of pressure on the structural, elastic, mechanical, and electronic properties of Cu2ZnSnS4 by means of first-principles calculations. The results indicate that both the lattice constant and cell volume decrease with an increase of pressure, which matches well with previously available values. Pressure has a more significant influence on the c direction than the a and b direction. The obtained elastic constants reveal the Cu2ZnSnS4 is mechanically stable between 0 GPa and 15 GPa. The bulk modulus, shear modulus, and Young’s modulus are evaluated by Voigt-Reuss-Hill approximation. All of these elastic moduli exhibit a monotonic feature as a function of pressure. The Poisson’s ratio, Pugh’s criterion, and Cauchy pressure indicate that the quaternary compound Cu2ZnSnS4 is ductile against pressure. Meanwhile, the analysis of the electronic structures reveals that the states near the valence band top are derived from Cu 3d and S 3p orbitals, and the lowest conduction band is composed of Sn 5s and S 3p orbitals. We expect that the findings which predicted the physical properties of this compound will promote future experimental studies on Cu2ZnSnS4.