Bayesian analysis for masked data under competing risk frameworks is studied for the purpose of assessing the impact of covariates on the hazard functions when the failure time is exactly observed for some subjects but only known to lie in an interval of time for the remaining subjects. Such data, known as partly interval-censored data, usually result from periodic inspection. Dirichlet and Gamma processes are assumed as priors for masking probabilities and baseline hazards. The Markov Chain Monte Carlo (MCMC) technique is employed for the implementation of the Bayesian approach. The effectiveness of the proposed model is tested through numerical studies, including simulated and real data sets.