This work is concerned with the determination of the effective propert
ies of transversely isotropic fiber composites made up of two rigid-pe
rfectly plastic phases in prescribed volume fractions. The phases are
assumed to satisfy incompressible, isotropic yield criteria of the Mis
es type. To study the behavior of these composites we make use of vari
ational principles, recently developed by Ponte Castaneda (1991, J. Me
ch. Phys. Solids 39, 45-71), that provide a method for generating esti
mates for the effective properties of nonlinear composites from corres
ponding estimates for the effective properties of linear composites. W
e demonstrate that this method allows us to obtain simple expressions
for the effective yield functions of rigid-perfectly plastic composite
s. Explicit results, corresponding to the Hashin-Shtrikman bounds, the
self consistent and the generalized self consistent estimates, and th
e composite cylinder assemblage model are obtained for the class of ri
gid-perfectly plastic fiber composites. These estimates exhibit the ex
istence of two distinct yielding modes, in agreement with correspondin
g experimental results.