The subject of this investigation is the stress evolution characteristics of rock impacted by transverse plain water jet (PWJ), including the application of stress evolution in the interpretation of the laws of breaking rocks (including artificial rock). Based on the semi-infinite plane theory, an analytical solution of the stress evolution of rock subjected to transverse jet loading is obtained, and the evolution of the stress state variable F of the rock microelement based on the Mohr–Coulomb criterion is also obtained. Then, elastic brittle failure and elastic-brittle damage of rock microelements are analyzed. Besides, an expression of the damage variable D based on elastic-brittle failure assumption is proposed. The analysis shows that the peak values of the F evolution curve determines the failure of the rock microelement based on the elastic-brittle failure hypothesis. The area SF surrounded by the evolution curve F and the line (F = F0) is positively correlated with the damage variable D, which can be used to qualitatively explain the time dependence of breaking rock using a transverse PWJ. In addition, the method based on damage variable D presented in this paper shows great potential in quantitative analysis of time dependence of rock failure.