  We study the $B_{1g}$ and $A_{1g}$ Raman profiles of M$_{2}$Cu$O_{4}$ (with
M= La, Pr, Nd, Sm, Gd), Bi$_{2}$Sr$_{2}$Ca$_{0.5}$Y$_{0.5}$Cu$_{2}$O$_{8+y}$%,
YBa$_{2}$Cu$_{3}$O$_{6.2}$ and PrBa$_{2}$Cu$_{2.7}$Al$_{0.3}$O$_{7}$ insulating
cuprates within the Loudon-Fleury theory, in the framework of an extended
Hubbard model for moderate on-site Coulomb interaction $U$. We calculate the
non-resonant contribution to these Raman profiles by using exact
diagonalization techniques and analyze two types of contributing mechanisms to
the line shapes: 4-spin cyclic exchange and spin-phonon interactions. Although
these interactions contribute to different parts of the spectra, together, they
account for the enhanced linewidth and asymmetry of the $B_{1g}$ mode, as well
as the non-negligible intensity of the $A_{1g}$ Raman line observed in these
materials.
