A capacity related reliability for transportation networks with random link capacity is introduced. It is defined as the probability that the road network can accommodate a certain level of traffic demand, and is built on the concept of network reserve capacity. Network reserve capacity is defined as the largest multiplier applied to an existing origin-destination demand matrix that can be allocated to a transportation network in a user-optimal way without violating the link capacities. Due to large variability associated with link capacities, a probabilistic approach is adopted to model the different physical and operational factors that often degrade the capacity of roadways. A Monte Carlo simulation procedure is developed to estimate the capacity related reliability measure. Numerical results are provided to demonstrate the feasibility of the approach.