Cut a small trough in the rice along the opposite edge of the nori from the open edge. Lay crab meat, slices of avocado and cucumber into the trough. Begin to close the roll from the trough side by curling the rolling mat over the ingredient-laden nori. Be careful not to compress the roll too much and create a hard rice log.
Dampen the uncovered edge of nori to help it stick to and seal the outside of the roll as it closes. When finished, let the roll sit for a few minutes before cutting.