  The problem of the sea wave runup on a beach is discussed in the framework of
the rigorous solutions of the nonlinear shallow-water theory. Key and novel
moment here is the accounting of the asymmetric waves when the face slope
steepness exceeds the back slope steepness. It is shown that the runup height
growth with increase of the face slope steepness meanwhile the rundown
characteristics are weakly depend from the face slope steepness. These results
explain why the tsunami waves with steep front (as during the 2004 tsunami in
the Indian Ocean) penetrate inland on large distances to compare with wave with
symmetrical shape.
