We use an off-lattice microscopic model for solutions of equilibrium polyme
rs (EP) in a lamellar shear flow generated by means of a self-consistent ex
ternal field between parallel hard walls, The individual conformations of t
he chains are found to elongate in flow direction and shrink perpendicular
to it while the average polymer length decreases with increasing shear rate
. The Molecular Weight Distribution of the chain lengths retains largely it
s exponential form in dense solutions whereas in dilute solutions it change
s from a power-exponential Schwartz distribution to a purely exponential on
e upon an increase of the shear rate, With growing shear rate the system be
comes increasingly inhomogeneous so that a characteristic variation of the
total monomer density. the diffusion coefficient. and the center-of-mass di
stribution of polymer chains of different contour length with the velocity
of flow is observed. At higher temperature, as the average chain length dec
reases significantly, the system is shown to undergo an order-disorder tran
sition into a state of nematic liquid crystalline order with an easy direct
ion parallel to the hard walls. The influence of shear flow on this state i
s briefly examined.