Coax cable shielding understanding at AC
But if the cycle is negative then it it will flow in the shielding,
  won't it?


In short, the polarity doesn't matter, but the field strength does. If you have two bare wires, one with 120V AC and one with the signal (lets say its an audio signal) the electric field will 'flow' from one to the other whenever the potential is not equal. The audio cable would only be a few volts, the AC would be changing from -120V at its peak to 120V and the electric field would want to flow to the audio cable (which would have a much lower voltage level of less than ±2V). When the AC line changed to it's negative cycle, the electric field would 'flow' from the audio cable to the AC line. 

Now lets say we hear a 60Hz hum (or 50 whichever country your in) on the audio cable, we replace it with a shielded audio cable and the hum goes away. It does this because the shield blocks the electric field.

In the picture below, it shows the electric field and a shield, if you put something inside of the shield, it will block the electric field from interfering with anything on the inside.


Source: https://education.pasco.com/epub/PhysicsNGSS/BookInd-1482.html

Regular shielding found on most cables does not protect from magnetic interference, but protects from electric field interference. All conductors attenuate magnetic interference, but do not stop it completely. To effectively shield from magnetic interference, you need special expensive materials, like mu metal, that have a large attenuation factor. But most of the time this isn't needed because magnetic fields fade with distance faster than electric fields so magnetic interference isn't usually needed (but I have seen it on some audio amplifiers).