Abstract: The general differenteal equations of unsymmetrecal progectile lateral motion torching the bore wall with the bourrelet have been developed in this paper. The pattens of symmetrical projectile motion touching the wall with the bourrelet have been studied. They have been compared with projectile motion that it had been assumed that its rotating band center traveled along the axis of the vore and the bourrelet touched the wall. The approaches reduing projectiles dispersion have been made.