The maximum number of non-vanishing and independent second order photoelastic coefficients required by the seven pentagonal and the two icosahedral point groups 5(C5),\(\bar 5\)(S10),\(\overline {10} \)(C5h),\(\overline {10} \) m2(D5h), 52(D5), 5m(C5v),\(\bar 5\) 2m(D5d); 235(I), 2/m\(\bar 3\)\(\bar 5\)(Ih)—that describe the quasicrystals symmetry groups in two and three dimensions—is obtained. The schemes of non-vanishing and independent coefficients have been calculated and listed. Finally the results of this group-theoretical study are briefly discussed.