  We study a $R^{2}$ model of gravity with torsion in a closed
Friedmann-Robertson-Walker universe. The model is cast in Hamiltonian form
subtracting from the original Lagrangian the total time derivative of
$f_{K}f_{R}$, where $f_{K}$ is proportional to the trace of the extrinsic
curvature tensor, and $f_{R}$ is obtained differentiating the Lagrangian with
respect to the highest derivative. Torsion is found to lead to a primary
constraint linear in the momenta and a secondary constraint quadratic in the
momenta, and the full field equations are finally worked out in detail.
Problems to be studied for further research are the solution of these equations
and the quantization of the model. One could then try to study a new class of
quantum cosmological models with torsion.
