The Markov chain model can be found in the maintenance and repair problems since the early 60's, is introduced to the maintenance of road infrastructure in the 1980's, and is made to drive the current bridge maintenance optimization systems. While this model results into solvable programming problems and provides a solution, there are a number of criticisms associated with it. In this article, we highlight the shortfalls of the Markov model for bridge infrastructure lifetime assessment and promote the use of stochastic processes. We use examples from a study for the modeling of the condition of bridges that considers more than 15 years of data. We argue for the applicability of the gamma process and other stochastic processes.