  We develop the analysis of finite element approximations of implicit
power-law-like models for viscous incompressible fluids. The Cauchy stress and
the symmetric part of the velocity gradient in the class of models under
consideration are related by a, possibly multi--valued, maximal monotone
$r$-graph, with $1<r<\infty$. Using a variety of weak compactness techniques,
including Chacon's biting lemma and Young measures, we show that a subsequence
of the sequence of finite element solutions converges to a weak solution of the
problem as the finite element discretization parameter $h$ tends to 0. A key
new technical tool in our analysis is a finite element counterpart of the
Acerbi--Fusco Lipschitz truncation of Sobolev functions.
