The two forces involved when a large heavy box rests on a flat floor are:

1. Gravity: This force pulls the box downwards towards the center of the Earth. It's the force that gives the box its weight.

2. Normal force: This is the force exerted by the floor on the box, acting perpendicular to the surface of contact. It acts in the opposite direction to gravity, preventing the box from falling through the floor.

These two forces are equal and opposite, resulting in a net force of zero and the box remaining stationary.