According to the theory of plate tectonics what forces cause the movement of plates in the earth's crust

Convection and gravity.

Explanation:

As we know, the earth's crust is positioned just above another layer of our planet: the mantle. It is basically composed of magma, which is nothing more than liquid rocks, with a slightly pasty consistency, all because of the high temperatures within the Earth. The tectonic plates literally float over the magma.

Thus, what makes the tectonic plates move is precisely the movement of this magma! And this movement does not happen at all, but in a cyclical variation, which we call Earth convection currents or cells.

In addition, tectonic plates can move under the influence of gravity, in a process called "Mesooceanic chain expansion push". In this case, the freshly formed plates in the mountain ranges are hot and therefore have higher heights than the more distant cold and dense plates; gravity causes the older plates to move away, that is, it causes movement.