We study the elastic properties of incommensurate solid 4He in the limit of zero temperature. Specifically, we calculate the pressure dependence of the five elastic constants (C11, C12, C13, C33, and C44), longitudinal and transversal speeds of sound, and the T=0 Debye temperature of incommensurate and commensurate hcp 4He using the diffusion Monte Carlo method. Our results show that under compression, the commensurate crystal is globally stiffer than the incommensurate, however at pressures close to melting (i.e., P∼25 bar) some of the elastic constants accounting for strain deformations of the hcp basal plane (C12 and C13) are slightly larger in the incommensurate solid. Also, we find that upon the introduction of tiny concentrations of point defects, the shear modulus of 4He (C44) undergoes a small reduction.