Cutouts are widely used to accommodate windows, openings for access purposes, or fasteners in the primary structural parts of airplanes. The presence of cutouts in composite panels results in stress or strain concentrations, leading to potentially reduced load-carrying capacity. Steering tows around cutouts using emerging techniques in three-dimensional (3-D) printing and advanced fiber placement can potentially alleviate such problems. Continuous tow steering around cutouts also eliminates fiber cutting, thereby precluding ply-level 3-D stress concentration, which could otherwise lead to delamination-induced damage. This work examines stress and strain concentrations, using continuous tow steering, around a representative wingbox access hole. Buckling response under compression loading together with stress and strain concentrations under both tensile and compression loads are examined. A steered configuration shows a 26% improvement in buckling performance in comparison with the equivalent straight-fiber configuration. Under tensile loading, the maximum stress and strain concentration factors around the cutout are 29 and 32% larger, respectively, for straight-fiber orientations than those with steered tows around the cutout. For the compression loading condition, the direct strain of the panel with straight-fiber orientations was found to be three times that of steered-fiber trajectories in the vicinity of the cutout.