Characterization of HIV viral rebound after the discontinuation of antiretroviral therapy is central to HIV cure research. We propose a parametric nonlinear mixed effects model for the viral rebound trajectory, which often has a rapid rise to a peak value followed by a decrease to a viral load set point. We choose a flexible functional form that captures the shapes of viral rebound trajectories and can also provide biological insights regarding the rebound process. Each parameter can incorporate a random effect to allow for variation in parameters across individuals. Key features of viral rebound trajectories such as viral set points are represented by the parameters in the model, which facilitates assessment of intervention effects and identification of important pretreatment interruption predictors for these features. We employ a stochastic expectation-maximization (StEM) algorithm to incorporate HIV-1 RNA values that are below the lower limit of assay quantification. We evaluate the performance of our model in simulation studies and apply the proposed model to longitudinal HIV-1 viral load data from five AIDS Clinical Trials Group treatment interruption studies.