A stochastic Direct Simulation Monte Carlo (DSMC) method has been extended for handling bubble-bubble and bubble-wall collisions. Bubbly flows are generally characterized by highly correlated velocities due to presence of the surrounding liquid. The DSMC method has been improved to account for these kind of correlated collisions along with a treatment allowing the method to be used also at relatively high volume fractions. The method is first verified with the deterministic Discrete Particle/Bubble Model (DPM/DBM) using two problem cases: (a) dry granular flow of particles through two impinging nozzles and (b) 3D periodic bubble rise for mono-disperse and poly-disperse systems. The verification parameters are the total number of prevailing collisions within the system, the collision frequencies and the time-averaged liquid velocity profiles (only for the 3D-periodic bubble rise). Subsequently the method is applied to a lab-scale bubble column and validated with the experimental data of Deen et al. (2001). A computational performance comparison with the DBM is reported for the 3D periodic bubble rise case with varying overall gas fractions. The DSMC is approximately two orders of magnitude faster than the deterministic approach for the studied dense bubbly flow cases without adverse effects on the quality of the computational results. (C) 2017 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license