A hybrid method combing molecular dynamics and two-step radiation heating model is used to study the kinetics and microscopic mechanisms of picosecond laser melting of monocrystalline copper in stress confinement regime. The nonequilibrium processes of laser melting are simulated by classical MD method, and laser excitation as well as subsequent relaxation of the conduction band electrons are described continually by two-step radiation heating model. The mechanism responsible for melting of copper under picosecond laser pulse irradiation can be attributed to homogeneous nucleation of the liquid phase inside the solid region. The speed of stress wave is predicted to be 4400m/s equal to that of sound. The liquid and crystal regions are identified definitely in the atomic configurations by means of Local Order Parameter, in-plane structure and number density of atoms. Velocity-reducing technique is proved efficient in avoiding the influence of the reflected stress wave on melting process by comparing two models with velocity-reducing technique and free boundary condition at the bottom respectively.