Analytically solving the first passage failure probability of the Wiener process is extremely significant. Therefore, this paper conducts research on the problem of the first passage of the Wiener process across the safety boundary based on the Monte Carlo simulation method. Firstly, the simulation ideas and steps of the Wiener process are elaborated, where the direct method for generating random numbers is adopted to implement Wiener process simulation in MATLAB. Then, taking concrete durability degradation following a Wiener process as an engineering case, the first passage failure probability is calculated using the Monte Carlo simulation method. Comparative analysis with mathematical analytical solutions demonstrates that the Monte Carlo method achieves computational accuracy comparable to analytical solutions, while exhibiting superior advantages in application scope and operational convenience. This research provides a numerical solution approach for calculating first passage failure probabilities using Wiener processes in relevant engineering fields.