We propose inference of the stress strength parameter, R=P(Y<X), when X and Y are independent generalized exponential-Poisson random variables. The problem of classical and Bayesian estimation of R is discussed. The Metropolis-Hastings algorithm is used to approximate the posteriors of R. Bayesian informative priors are considered under symmetric and asymmetric loss functions. Asymptotic confidence intervals for R are proposed. Monte Carlo simulations are performed to compare the proposed methods. At the end, a real dataset is analyzed for illustrative purposes.