The propagation in water of nanosecond focused laser pulses having power densities up to terra watts / cm2 and wavelength of 532±2nm, has been investigated extensively by our group. Fast imaging as well as time resolved photography of the nonlinear optical processes, revealed the formation of running spherical foci as well as luminous cavitation bubbles along the direction of the propagating beam. Associated mechanical effect of shock pressure was measured at the exit window as soon as the bubbles collapsed, using piezoelectric silicon gauge. The lifetime of the luminous cavitation bubbles and running spherical foci were found to vary between 160 to 50 ps. Their propagation velocities were estimated to be of the order of 106 m/s. The results are discussed and could be explained partially according to the Moving Focus Model, the self‐phase Modulation Model and other associated processes.