Streaks in rectangular-jet flows are modeled using resolvent analysis, providing insight into the underlying physics of coherent structures. Two-dimensional, cross-plane resolvent analysis is used to evaluate the most-amplified coherent structures at very low frequencies. The highest-gain mode exhibits a large dipole-like structure, featuring a high-speed streak on one major-axis edge of the jet and a low-speed streak on the other, while the second-highest gain mode is the minor-axis-aligned counterpart. Higher-order modes exhibit finer streak spacing, resembling boundary layer modes. Varying the curvature of the jet corners has minimal impact on the gains and mode shapes, suggesting corner vortices in real rectangular-jet flows may not be primarily caused by free-shear streak formation, at least under the modeling hypothesis. Increasing shear thickness typically decreases gains and disperses mode shapes but sensitivity to the forcing weighting method is evident. Increasing the aspect ratio increases the gains for all modes except for the leading dipole-type modes which exhibit a monotonic decrease. The position of streaks relative to the corners changes with aspect ratio causing some complicated gain dependence.