We show in this paper that intermediate shocks are formed from kinetic Alfven waves through wave form continuous steepening. From the action of nonlinear interaction and dispersion Alfven solitons are formed and then evolve into shocks. We calculated the traveling stationary structures directly from nonlinear autonomous equations which we had derived. These traveling stationary structures correspond to intermediate shock, switch-on shock or Alfven solitary waves. Another kind of rare discontinuity was discovered in the calculation from the rarefying solitary waves. The solitary wave series remain on the front of the shocks because of no strong dissipation appears in the equation. When we added some anomalous dissipation terms to the equations, intermediate shocks with increased in entropy appeared.