A Tweedie regression model with random effects is applied to claims reserving in general insurance. The parameter estimates are obtained by following two different approaches: the one in Ohlsson, Johansson (2006), which combines generalized linear models with credibility, and the hierarchical generalized linear models approach (Lee, Nelder (2001)). In both cases the claims reserves and the estimation errors are evaluated. A numerical example illustrates the two approaches.