We investigate some modifications to the Press & Schechter ( 1974 ) ( PS ) prescription resulting from shear and tidal effects .
These modifications rely on more realistic treatments of the collapse process than the standard approach based on the spherical model .

First , we show that the mass function resulting from a new approximate Lagrangian dynamic ( [ Audit & Alimi 1996 ] ) , contains more objects at high mass , than the classical PS mass function and is well fitted by a PS-like function with a threshold density of \delta _ { c } \simeq 1.4 .
However , such a Lagrangian description can underestimate the epoch of structure formation since it defines it as the collapse of the first principal axis .
We therefore suggest some analytical prescriptions , for computing the collapse time along the second and third principal axes , and we deduce the corresponding mass functions .
The collapse along the third axis is delayed by the shear and the number of objects of high mass then decreases .

Finally , we show that the shear also strongly affects the formation of low-mass halos .
This dynamical effect implies a modification of the low-mass slope of the mass function and allows the reproduction of the observed luminosity function of field galaxies .
In a companion paper , we present results of numerical simulations which complete this work .