To track extended targets for the linear Gaussian system, the multiple extended target Rao-Blackwellised particle filter (RBPF), which estimates the data association and multiple target states jointly, is proposed. The proposed filter applies the particle filter to estimate the data association, and employs the extended target filter based on random matrix to estimate kinematic states and shape information of extended targets. First, the framework of the multiple extended target RBPF is proposed. Then, the joint proposal distribution for the association hypothesis is defined. Furthermore, the Bayesian framework of multiple extended target tracking is implemented by the combined filter, which applies the particle filter and the extended target filter based on random matrix. In comparison with the multiple extended target filter based on JPDA algorithm and the multiple extended target filter based on probability hypothesis density, simulation results show that the multiple extended target RBPF achieves the less error of the shape estimates, and enhances the position tracking accuracy in the situation that there are spatially close extended targets.