This paper aims to determine, for the period of institutional control (300 yr), the probability of occurrence of the net release scenario of radioactive waste from a near-surface repository. The radioactive waste focused on in this work is that of low and medium activity generated by a pressurized water reactor plant. The repository is divided into eight modules, each of which consists of six barriers (top cover, upper layer, packages, base, walls, and geosphere). The repository is a system where the modules work in series and the module barriers work in active parallel. The module failure probability for radioactive elements is obtained from a Markov model because of shared loads assumed for the different barriers. Lack of field failure data led to the necessity of performing sensitivity analyses to assess the failure rate impact on module and barrier failure probabilities. Module failure probabilities have been found to be lower for those radioactive elements with higher retardation coefficients. The geosphere mean time to failure is the most important parameter for calculating module failure probabilities for each radioactive element. The repository module has presented higher failure probabilities for iodine, technetium, and strontium. For iodine, the estimated probability is 16% for 300 yr and 96% for 1000 yr. The basis for performance evaluation of the deposition system is the understanding of its gradual evolution. There are many uncertainty sources in this modeling, and efforts in this direction are strongly recommended.