A numerical simulation is conducted for a blood flow in a capillary vessel, including not only red blood cells (RBCs)-like elastic membranes but also platelets-like elastic solids. Recently-developed full Eulerian approaches for coupling with a fluid and elastic solid/membrane are employed for dealing with dynamic interactions of the RBC, platelet and vessel wall. A pressure-induced periodic flow is imposed on a suspension of the RBCs and platelets with a hematocrit of 20 %, and then the simulation is run up to a certain time at when the flow is developed well. Numerical results indicate that a relative apparent viscosity in the suspension of the RBCs and platelets increases, and a platelet motion is strongly affected by the presence of the RBCs.