The ground and a few excited states of the beryllium atom in external unifo
rm magnetic fields are calculated by means of our 2D mesh Hartree-Fock meth
od for field strengths ranging from zero up to 2.35 x 10(9) T. With changin
g field strength the ground state of the Be atom undergoes three transition
s involving four different electronic configurations which belong to three
groups with different spin projections S-z = 0, -1, -2. For weak fields the
ground state configuration arises from the 1s(2)2s(2), S-z = 0 configurati
on. With increasing field strength the ground state evolves into the two S-
z = -1 configurations 1s(2)2s2p(-1) and 1s(2)2p(-1)3d(-2), followed by the
fully spin polarised S-z = -2 configuration 1s2p(-1)3d(-2)4f(-3). The latte
r configuration forms the ground state of the beryllium atom in the high fi
eld regime gamma > 4.567. The analogous calculations for the Be+ ion provid
e the sequence of the three following ground state configurations: 1s(2)2s
and 1s(2)2p(-1) (S-z = -1/2) and 1s2p(-1)3d(-2) (S-z = -3/2).