Abstract: In practical applications of damped elastic systems, the model under investigation is influenced by variations caused by white noise and environmental factors.These stochastic elements can significantly affect the outcomes of model simulations.Compared to traditional damped elastic systems, this type of system is more complex due to the inclusion of stochastic terms, which presents considerable challenges for theoretical analysis.In order to address this challenge, this paper will employ stochastic analysis as a tool to provide insights into the existence of mild solutions for stochastic elastic systems with damping in Hilbert space.In the specific research process, we first skillfully employ the monotone iteration technique and operator semigroups theory to construct the mild solution of the system under investigation.This initial step establishes a solid theoretical foundation for the subsequent in-depth analysis.Following this, we utilize stochastic analysis theory, Hölder inequality, and the fixed point theorem to address the case of non-Lipschitz continuity of the nonlinear terms.After a series of rigorous derivations and arguments, we ultimately obtain the existence result of the mild solution for the studied system.This finding significantly supplements and extends the existing theory of damped elastic systems.