A two-dimensional model of a tethered capsule is used to elucidate the effects of capsule aspect ratio and capsule internal viscosity on capsule dynamics. Over the parameter space examined, the capsule initially elongates out into the flow and then slowly pivots toward the wall as the capsule relaxes to a steady-state shape. The region of the capsule membrane that would come into contact with the wall corresponds with a region of elevated traction-force magnitude. The effect of viscosity is found to be negligible at low shear rates, but at high shear rates, an increase in internal viscosity leads to an increase in the maximum capsule deformation and maximum force on the tether. At low shear rates, capsules with higher aspect ratios experience less force and deformation. Conversely, at high shear rates, capsules with higher aspect ratios experience greater force and deformation.