In the present paper, the stability of Coalescence Hidden variable Fractal
Interpolation Surfaces(CHFIS) is established. The estimates on error in
approximation of the data generating function by CHFIS are found when there is
a perturbation in independent, dependent and hidden variables. It is proved
that any small perturbation in any of the variables of generalized
interpolation data results in only small perturbation of CHFIS. Our results are
likely to be useful in investigations of texture of surfaces arising from the
simulation of surfaces of rocks, sea surfaces, clouds and similar natural
objects wherein the generating function depends on more than one variable.