<p>Uncertainty theory has been verified to effectively address the epistemic uncertainty owing to lack of experience or knowledge. Based on uncertainty theory, we concentrate on the reliability analysis for uncertain wave equation model which is used to describe the propagation of waves. Firstly, we probe into the uncertainty distribution pertaining to the first hitting time of the uncertain wave equation and devised a numerical algorithm aimed at deriving the uncertainty distribution of the first hitting time. Additionally, there is a broad consensus within the academic community that the first hitting time serves as a type of fundamental analytic tool for addressing reliability assessment of dynamic systems. Thus, by using fist hitting time, we propose belief reliability function and belief reliable lifetime for assessing the reliability of uncertain wave equation model. Moreover, for discussing the belief reliability function and belief reliable lifetime, we consider two special cases of the uncertain wave equation model: one is under fixed force and the other is under periodic force. Eventually, we verify the validity of belief reliability function and belief reliable lifetime for uncertain wave equation model by using some examples.</p>