  The theory of plastic bending of single crystal beam having two active slip
systems is proposed. Applying the variational-asymptotic method we reduce the
energy functional of the beam to the one-dimensional energy functional which
admits analytical solutions for the symmetric slip systems. The threshold value
at the onset of plastic yielding, the dislocation density, as well as the
moment-curvature curve are found. We solve also a similar problem that takes
the energy dissipation into account.
