Vibroflotation is a method of ground improvement up to depths of 40 metres. It has been successfully used since 1936 but the major problem with this method is that in spite of the fact that it performs well, nobody can explain how it works. The techniques for checking the quality of the compaction during vibration are unreliable, making the method as a whole unquantifiable and unmeasurable. This title explores the problems surrounding the method, looking at deep compaction, plastodynamics and the Riemann problem amongst other issues, showing the reader what information from the movement of the vibration can be used as an additional quality control and to assess effectiveness.