Boundary contours are important for representing binocular surfaces, including those in binocular rivalry. Ooi and He (2006, Perception 35 581-603) showed that a half-image with a boundary contour defined by abutting gratings predominates in binocular rivalry. We investigated the monocular-boundary-contour mechanism using Kanizsa square-like rivalry displays. In experiment 1, the left half-image had a vertical illusory contour on the right edge while the right half-image had a vertical illusory contour on the left edge. The Kanizsa elements (discs and pacmen) were filled with a 135 degree grating and placed on a 45 degree-grating background. When fused, observers experienced a strong predominance for perceiving an illusory rectangle in front of four discs. But this percept was replaced by robust rivalry alternations when the stimulus was manipulated by (i) switching the half-images between eyes, (ii)relocating the pacmen in each half-image to form horizontal illusory contours, or (iii) placing the pacmen diagonally (thus eliminating each monocular illusory contour). Such robust rivalry alternations were similar to those experienced when a 135 degree-grating disc was in rivalry with a 135 degree-grating pacman alone on the 45 degree-grating background (experiment 2). Experiment 3 showed that the relatively stable illusory-rectangle percept in experiment 1 is affected by the alignment of the images in the two eyes, in a manner consistent with adherence to the occlusion constraint in binocular surface formation.