Elastic turbulence is a flow instability that occurs in polymer solutions at low Reynolds numbers and is hypothesized to play an important role in processes such as enhanced oil recovery. Although elastic turbulence is well-established as a phenomenon both experimentally and theoretically, there are open questions about how polymer properties influence the transition to turbulence and the characteristics of the resulting flows. We are developing particle-based simulation models that are well-suited for addressing these questions. We first simulate the flow of a Newtonian fluid in expansion–contraction microchannels, which are known to produce elastic turbulence, using both dissipative particle dynamics and multiparticle collision dynamics (MCPD). We compare the average flow field and volumetric flow rate measured in the particle-based simulations to an analytical approximation (regular perturbation theory) and a numerical solution (boundary integral method), finding excellent agreement. We then simulate flow of a polymer solution in a rotating cylinder geometry using MPCD. We characterize deviations of the flow from laminar behavior for different polymers and flow conditions, seeking to identify signatures of elastic turbulence. Our particle-based models open new possibilities for simulating elastic turbulence for the different types of polymers used in various energy and environmental applications.