Put a large pan with salted water on high heat and bring to a boil. Rinse the rice in a colander under running water until the water runs clear. Add rice to the boiling water and boil for around 12 minutes. Remove from the heat, drain in a colander, and set aside to cool.
Prepare 15 small bowls or glasses. On the bottom of each, place the following layers: rice, tuna, and zucchini. Season with salt and pepper. Dollop or pipe on some mayonnaise and serve immediately.