  Assuming that the early optical emission is dominated by the external reverse
shock (RS) in the standard model of gamma-ray bursts (GRBs), we intend to
constrain RS models with the initial Lorentz factor $\Gamma_0$ of the outflows
based on the ROTSE-III observations. We consider two cases of the RS behavior:
the relativistic shock and the non-relativistic shock. For homogeneous
interstellar medium (ISM) and wind circum-burst environment, the constraints
can be achieved by the fact that the peak flux $F_{\rm \nu}$ at the RS crossing
time should be lower than the observed upper limit $F_{\rm \nu,limit}$. We
consider the different spectral regimes that the observed optical frequency
$\nu_{\rm opt}$ may locate in, which are divided by the orders for the minimum
synchrotron frequency $\nu_{\rm m}$ and the cooling frequency $\nu_{\rm c}$.
{\bf Considering the homogeneous and wind environment around GRBs, we find that
the relativistic RS case can be constrained by the (upper and lower) limits of
$\Gamma_0$ in a large range from about hundreds to thousands for 36 GRBs
reported by ROTSE-III. The constraints on the non-relativistic RS case are
achieved with limits of $\Gamma_0$ for 26 bursts ranging from $\sim 30$ to
$\sim 350$.} The lower limits of $\Gamma_0$ achieved for the relativistic RS
model is disfavored based on the previously discovered correlation between the
initial Lorentz factor $\Gamma_0$ and the isotropic gamma-ray energy $E_{\rm
\gamma, iso}$ released in prompt phase.
