Stereo matching, utilized in diverse fields, poses a challenge to systems in resource-constrained environments due to the significant growth of computational load with image resolution. The challenge is crucial for the systems because fields utilizing stereo matching require short operational time for real-time applications and low power architecture. Stochastic computing (SC) is able to be a valuable approach to address the challenge by reducing the computational load by representing binary numbers with stochastic sequences, which are encoded as a probability value, and by leveraging the concept of mathematical probability. Also, it is possible for a system to be error-tolerant by utilizing the characteristics of stochastic computing. Therefore, in this paper, we propose an approach for lightweight and error-tolerant stereo matching with a hardware-implemented stochastic computing processor. To verify the feasibility and error tolerance of the proposed system, we implemented the proposed system and conducted experiments comparing depth maps with or without stochastic computing by calculating similarities. According to the experimental results, the proposed system indicated no significant differences in output depth maps and achieved an improvement in the depth maps from error-injected input images by an average of 58.95%. Therefore, we demonstrated that stereo matching with stochastic computing is feasible and error-tolerant.