  Among several analytic approximations for the growth of density fluctuations
in the expanding Universe, Zel'dovich approximation in Lagrangian coordinate
scheme is known to be unusually accurate even in mildly non-linear regime. This
approximation is very similar to the Pad\'e approximation in appearance. We
first establish, however, that these two are actually different and independent
approximations with each other by using a model of spheroidal mass collapse.
Then we propose Pad\'e-prescribed Zel'dovich-type approximations and
demonstrate, within this model, that they are much accurate than any other
known nonlinear approximations.
