Here's what happens to aircraft with elevators as they start going supersonic...

1) Transonic Region

Mach tuck happens when aircraft transition through the transonic region, which can be anywhere from 0.75 Mach to 1.2 Mach.

2) Critical Mach Number

You reach MCrit, or your critical mach number, when the first molecule of air reaches the speed of sound over the aircraft (this can be over the wing, or any other part of the aircraft). When this happens, shockwaves start to form, changing aircraft handling characteristics and overall performance.

3) Aerodynamic Center

As the aircraft transitions through the transonic region and shockwaves become larger, the aerodynamic center on the wing moves aft, towards the trailing edge of the airfoil.

4) Shock Wave On The Wing

As air flows from the supersonic region in front of the shockwave, to the subsonic region behind the shockwave, it separates and becomes turbulent.

5) Loss Of lift

As the shockwave becomes stronger, more airflow separation occurs, known as wave drag. This creates an overall reduction in lift on the airfoil.

6) Shock Wave On The Horizontal Stabilizer

This forms for the same reason as the shockwave on the wing, however, this time you have a control surface that is located directly behind the shockwave...the elevator.

7) Loss Of Elevator Effectiveness

Due to the reduction in lift (and downwash) from the main wing, as well as the aft movement of the aerodynamic center, the aircraft requires more back pressure on the elevator in order to prevent the nose from dropping.

8) The "Tuck"

No matter how much back pressure is applied, the elevator is now located in a region of aerodynamically "dead" air, rendering the elevator ineffective. Without an elevator, the airplane starts an uncontrolled dive. As the airspeed increases in the dive, the shockwave becomes more aggressive, and the situation becomes worse.

To prevent this from happening, most supersonic aircraft are equipped with stabilators, not elevators (more on that here).

And many high-subsonic aircraft are equipped with vortex generators on their elevators, to energize airflow and prevent airflow separation.