We use molecular dynamics to study the structure of steady shock waves with melting transition traveling along the 100 , 110 , and 111 directions in the Lennard-Jones (L-J) perfect fcc crystal. Unlike shock waves in gases and fluids, solid shocks exhibit oscillatory behaviour of profiles within the front that persists even in the strong shocks with melting. Surprisingly, shock wave along the 100 direction compresses the L-J crystal to the final overheated solid state in contrast to 110 and 111 cases wherein the crystal melted at the same shock velocity us = 4.39 km/s. Moreover, the 110 and 111 melting shock waves differ widely in the front structure: the 111 profile without oscillations is closely similar to that of the fluid shocks, whereas the 110 shock exhibits a steady precursor of solitary wave train. The evolution of velocity and pair distribution functions across the shock layer are explored to study the shock-induced structure transformations and melting transition occuring within the region of length roughly (10 ÷ 30) σ, σ = 3.405Ȧ. §1. IntroductionThe purpose of this paper is to address one of the important questions in physics of shock waves in solids: that is, what are the properties of nonequilibrium layer where the material transforms in going from the initial state in front of the shock to the final high-pressure and high-temperature equilibrium state behind the shock ? Understanding the internal structure of a shock wave is crucial to the development of appropriate continuum constitutive models as well as theoretical treatments of shock-induced phenomena, such as detonation. 1) This problem calls for high resolution in time-and space-measurements, and it is particularly well approached by the molecular dynamics (MD) simulation method.Previous MD studies of shock waves in solids have been primarily devoted to the simulation of shocks traveling along the 100 direction in fcc Lennard-Jones perfect crystal 2), 3) and demonstrated that the microscopic mechanism of their propagation is inherently more complex because plastic flow is governed by creation and motion of defects, not by viscous dissipation as in fluids. Owing to specially developed techniques for MD simulation in the reference frame of the shock which greatly reduces the statistical noise, we have found an oscillatory behaviour of 100 profiles within the shock front (also reported in certain of early simulation works 2) although not observed in subsequent studies) and examined it in close details. 4) It is suggested * )