The shear modulus of solid He4 exhibits an anomalous increase at low temperatures that behaves qualitatively similar to the frequency change in torsional oscillator experiments. We propose that this stiffening of the shear modulus with decreasing temperature can be described with a glass susceptibility assuming a temperature-dependent relaxation time τ(T). Below a characteristic crossover temperature TX, where ωτ(TX)∼1, a significant slowing down of dynamics leads to an increase in the shear modulus. We predict that the maximum change of the amplitude of the shear modulus and the height of the dissipation peak are independent of the applied frequency ω. Our calculations also show a qualitative difference in behavior of the shear modulus depending on the temperature dependence of τ(T).