Numerical modeling of fast Z-pinch dynamics which allows for effects o
f electron magnetohydrodynamics is discussed; of these, the most impor
tant manifestation proves to be nonlinear convective penetration of fi
eld (current) into the plasma of Z-pinch. This highly nontrivial dynam
ics can be modeled using a relatively simple modification of the diffu
sion equation for magnetic field and the equation of heating of plasma
particles. Two models of this type are suggested - for a one-scale pi
nch and for a thin liner. As a consequence, this opens possibilities o
f numerical modeling of processes that involve the effects of electron
magnetohydrodynamics on the basis of reliable, simple, and well-opera
ting MHD codes.