  I study the role of shear fields by using an analytical approximate solution
for the equations of motion of homogeneous ellipsoids embedded in a homogeneous
background. The equations of motion of a homogeneous ellipsoid (Icke 1973;
White & Silk 1979 (hereafter WS)) are modified in order to take account of the
tidal field as done in Watanabe 1993 and then are integrated analytically,
similarly to what done in WS. The comparison of the analytical solution with
numerical simulations shows that it is a good approximation to the numerical
one. This solution is used to study the evolution of the configuration ofthe
ellipsoids, to calculate the evolution of the density contrast and that of the
axial peculiar velocity of the ellipsoids for several values of the amplitude
of the external tidal field, and compared again with numerical simulations. In
order to calculate the evolution of the density contrast at turn-around and
collapse velocity at the epoch of collapse, as a function of the ratio of the
initial value of the semi-axes, I use the previously obtained approximate
solution to modify the analytical model proposed by Barrow & Silk (1981) for
the ellipsoids evolution in the non-linear regime. The density contrast at
turn-around and the collapse velocity are found to be reduced with respect to
that found by means of the spherical model. The reduction increases with
increasing strength of the external tidal field and with increasing initial
asymmetry of the ellipsoids. These last calculations are also compared with
numerical solutions and they are again in good agreement with the numerical
ones.
