Abstract: Penetration mechanics is important both as a scienceand in practice of military engineering. For a quasi-steady penetration of long rodprojectile into semi-infinite thick target, a simplified model isdeveloped, where the bullet incorporated mushroom head consists of unbrokenzone, crush zone and hole dilating zone, and the target consists of holedilating zone, crush zone and unbroken zone, with the strain rate effectbeingconsidered. A set of ODE is obtained through conservation laws of everypart. Through theoretical analysis and calculation, the influences of the crush strain rate, crash strength of the projectile and thestrain rate effect of the crash strength of the target on penetration depthare analyzed. The excellent agreement of the calculation results and theexperiment shows the effectiveness of the simplified model.