  On the basis of a three orbital model and an effective attractive interaction
between electrons we investigate the possible superconducting states, with $p$
and $f$-wave internal symmetry, of Sr$_2$RuO$_4$. For an orbital dependent
interaction which acts between in plane and out of plane nearest neighbour
Ruthenium atoms we find a state for which the gap in the quasi-particle spectra
has a line node on the $\alpha $ and $\beta $ sheets of the Fermi Surface, but
it is complex with no nodes on the $\gamma$-sheet. We show that this state is
consistent with all the available experimental data. In particular, we present
the results of our calculations of the specific heat and penetration depth as
functions of the temperature.
