  A precise measurement of the angle $\alpha$ in the CKM triangle is very
important for a complete test of Standard Model. A theoretically clean method
to extract $\alpha$ is provided by B$^0 \to \rho \pi$ decays. Monte Carlo
simulations to obtain the BTeV reconstruction efficiency and to estimate the
signal to background ratio for these decays were performed. Finally the
time-dependent Dalitz plot analysis, using the isospin amplitude formalism for
tree and penguin contributions, was carried out. It was shown that in one year
of data taking BTeV could achieve an accuracy on $\alpha$ better than
5$^{\circ}$.
