Lay the Nori sheets out on a flat rolling surface. Spread the sushi rice evenly over the sheets or seaweed, and sprinkle the sesame seeds over the surface.

Place the crabmeat and mayonnaise in a small bowl and mix until well combined.

Spread the crabmeat mixture evenly down the center of each Nori roll, and top with avocado and cucumber slices.

Roll the sushi into a log jelly-roll style. Slice into 3/4-inch pieces and serve immediately.