The leading order solution for the power law creep of a matrix around
a rigid finite fiber is developed. The matrix is well bonded to the fi
ber but the interface is assumed to be capable of slip with a drag whi
ch is linearly proportional to the slip velocity. In addition, mass tr
ansport by stress driven diffusion is assumed also to be possible at t
he interface between the fiber and the matrix. It is found that when t
here is no slip or interface mass transport, the composite has a high
creep strength compared to the matrix. However, both slip and mass tra
nsport acting individually or together are capable of reducing the cre
ep strength of the composite material. If slip occurs very readily or
mass transport is very rapid or both, the creep strength of the compos
ite can fall below that of the pure matrix material. It is notable tha
t mass transport and interface slip with a linear theology have an ide
ntical effect on the creep strength of the composite material.