The linewidth of the electron spin resonance (ESR) spectra for H impurities trapped in solid para-hydrogen is calculated. The equation for the linewidth, which was originally formulated for F-center problems, is modified to take account of the changes of the molecular hydrogen electronic orbitals, as well as the vibrations and rotations of the H-2 molecules. By virtue of constant pressure path integral Monte Carlo simulations, it is found that zero point vibrations make solid hydrogen so compressible that the solid cannot sustain the local stress created by interstitial impurities. As a result, the local environment for an impurity at an interstitial site is the same as that for an impurity at a substitutional site, and the calculated ESR linewidth for a H impurity in either site is the same and in excellent agreement with the experimental observation.