In this paper, the finite element method has been applied to solve fre
e and forced vibration problems of isotropic and laminated composite s
hells with and without cutouts employing the eight-node isoparametric
finite element formulation. Specific numerical problems of earlier inv
estigators are solved to compare their results. Moreover, free vibrati
on problems of cylindrical, spherical, saddle (hyperbolic paraboloid b
ounded by parabolas), hypar (hyperbolic paraboloid bounded by straight
lines), and conoidal shells with cutouts and forced vibration of comp
osite hypar and conoidal shells without cutouts are examined to arrive
at some conclusions useful to the designers. Eccentrically positioned
cutouts and transient stresses are other aspects studied in detail in
free and forced vibration analyses, respectively.