We prove the existence of a solution to a free boundary problem modeling blood flow in viscoelastic arteries. The model equations are obtained using asymptotic reduction from the incompressible, viscous Navier-Stokes equations, coupled with the linearly viscoelastic membrane equations. The reduced, effective equations are defined on the cylindrical geometry. The resulting problem is nonlinear with a free boundary. The existence of a weak solution is obtained by using the fixed point arguments.