  {\bf Abstract}: The existence of 2-dimensional KAM tori is proved for the
perturbed generalized nonlinear vibrating string equation with singularities
$u_{tt}=((1-x^2)u_x)_x-mu-u^3$ subject to certain boundary conditions by means
of infinite-dimensional KAM theory with the help of partial Birkhoff normal
form, the characterization of the singular function space and the estimate of
the integrals related to Legendre basis.
