A quark (Q) model of photoproduction of positive- and negative-parity baryons in association with a meson octet is proposed. According to this model, the basic mechanism for photoproduction is represented by a U-spin-invariant process γ+Q-->Q+Π at each quark, Π being a meson octet. The matrix elements of this basic amplitude are taken between appropriate 3Q states representing the initial proton and a final baryon, according to the multiplet structure 56+ of SU(6) and (70,(70,3)- of SU(6)⊗O(3) for the positive-parity and negative-parity baryonic states, respectively. The SU(3) sum rules based on U-spin invariance of the amplitudes are verified. Several additional sum rules, valid separately for spin-flip and non-spin-flip amplitudes, are derived for the 56+ states. For the negative-parity states, a number of nontrivial sum rules connecting different SU(3) multiplets are obtained.