The strong electric field at the surface of a strange star is discusse
d, and a self-consistent model is proposed to calculate its capability
of supporting a ''normal'' nuclear material crust. We find that the e
lectric field is already not able to support the crust even when the b
ottom density of the crust is still considerably lower than the neutro
n drip point, which means that it is not the neutron drip effect that
limits the maximum crust density of a strange star. The maximum crust
density is probably only about 8.3 x 10(10) g cm(-3), so that a typica
l strange star (1.4 M.) can not have a crust more massive than similar
to 3.4 x 10(-6) M.. Considerable limitations are also presented for s
trange dwarfs.