Аннотация:In usual dispersive quadratic nonlinear media self‐focusing (SF) does not exist. In recent years thermal SF of quasimonochromatic waves in highly viscous liquids like glycerin and thermal SF of sawtoothlike waves in inviscid fluids were observed experimentally. However both phenomena are very inert (characteristic stabilization time at least of order 10 s). A general question in nonlinear wave theory is whether inertialess SF in cubic nonlinear media without dispersion can exist (e.g. for shear waves). An acoustic beam in a cubic medium can be described by a modified KZK‐type equation. It is common practice to seek a solution (following the approach in nonlinear optics) in the form of a harmonic wave with slowly varying amplitude A. A nonlinear Schrödinger equation can be obtained for A which describes the increase in A due to plane front instability. However A decreases due to nonlinear absorption. To investigate the real behavior of the wave a more appropriate analytical approach together with computer methods were used. It was shown that SF has remarkable features. One can observe a marked decrease of the beamwidth. The increase in A however cannot be considerable.