One type of blood disease is a narrowing of a tubular structure, known as constriction or stenosis and high cholesterol is one of the main causes for this. Suitable mathematical models are important to describe this phenomenon, and to study the problem analytically and numerically. An approximate analytical solution and a recently developed particle-based method called multi-particle collision dynamics (MPC) is used to simulate the weakly compressible steady flow through a three-dimensional constricted axisymmetric cylinder. The particle collisions in MPC dynamics are numerically more efficient than other particlebased simulation methods. Particle interactions with the cylinder walls are modeled using slip as well as no-slip boundary conditions. Using an appropriate averaging procedure allows us to make a comparison between the approximate analytical solution and the numerical results. Significant and interesting differences were found in the velocity profiles obtained analytically and by using MPC.