Abstarct: Due to the complexity of appropriate statistical models for Bayesian analysis of recurrent event data‎, ‎we need to use sampling-baxsed methods such as MCMC algorithms‎. ‎However‎, ‎MCMC methods applied to these models come with a wide range of problems in terms of convergence‎, ‎mixing properties and computational time‎. ‎An alternative method is integrated nested Laplace approximation (INLA) method‎, ‎introduced by Rue et al‎. ‎(2009)‎. ‎The INLA method is very fast and does not suffer the same problems as MCMC‎. ‎Moreover‎, ‎the approximations described by INLA to be extremely accurate so that‎, ‎in order for any bias to be detected‎, ‎the MCMC algorithm would have to run for much longer time than it is usually done in practice‎. ‎In this thesis‎, ‎we assume that recurrent events occur according to a non-homogeneous Poisson process and then perform approximate Bayesian inference using INLA‎. ‎We illustrate our approach using both simulated and real life data‎.