The boundary value problem of a two-dimensional viscoelastic beam clamped at two ends and subjected to both a dead load and normal surface traction is solved using a finite element method here in Part B. The constitutive relationship between stress and strain developed in Part A uses a convected coordinate system and body tensor mathematics. Maxwell elements (springs and dashpots) describe the material for both fluid and solid characterizations. The overall finite element results calculated were physically reasonable. However, the assumed boundary conditions produce a stress singularity at the boundary, a singularity that is also seen in small deformation elastic theory.