  We study the origin of spin-gap in recently discovered material CaV$_4$O$_9$.
We analyze the spin-$1/2$ Heisenberg model on the $1/5$ depleted square lattice
with nearest neighbor (nn) and next nearest neighbor (nnn) interactions, in
terms of the singlet and triplet states of the 4-spin plaquettes and 2-spin
dimers. Phase diagram of the model is obtained within a linear
``spin-wave"-like approximation, and is shown to agree well with the earlier
results of QMC simulations for nn interactions. We further propose that the
special lattice structure of CaV$_4$O$_9$ naturally leads to lattice
distortions, which enhances the spin-gap via a spin-Peierls mechanism.
