Results from torsional stress relaxation experiments in which we measure the torque and normal force responses of two glassy poly(alkyl methacrylate)s are presented. Tests were performed at temperatures ranging from the dynamic glass transition (α-relaxation) to the first sub-glass transition relaxation (β-relaxation) and in the sub-yield range of deformations (strains ranging from 0.02 to 0.045) and at a fixed aging time of 4980 s. We found a significant difference between the relaxation behavior of the normal force response and the torque response of poly(methyl methacrylate) (PMMA). The results provide evidence that the normal force of PMMA is influenced by the β-relaxation, For specimens having a longer side chain length, i.e., poly(ethyl methacrylate) (PEMA), the difference between the normal force and torque relaxation behaviors is less. This is consistent with the less pronounced β-relaxation mechanism in PEMA. Furthermore, an examination of the effect of temperature on the ratio of the normal force modulus to the shear modulus of PMMA provides strong evidence that the normal force modulus relaxes faster than the shear modulus as the β-relaxation is approached. Also, following the scaling law relations of Penn and Kearsley, the derivatives of the strain energy density function with respect to the first and second invariants of the strain tensor were determined. Finally, the departure of the strain energy density function behavior of PMMA and PEMA from the neo-Hookean material behavior is shown.