  We develop the frame-like formulation of massive bosonic higher spins fields
in the case of 3-dimensional $(A)dS$ space with the arbitrary cosmological
constant. The formulation is based on gauge-invariant description by involving
the Stueckelberg auxiliary fields. The explicit form of the Lagrangians and the
gauge transformation laws are found. The theory can be written in terms of
gauge-invariant objects similar to the massless theories, thus allowing us to
hope to use the same methods for investigation of interactions. In the massive
spin 3 field example we are able to rewrite the Lagrangian using the new the
so-called separated variables, so that the study of Lagrangian formulation
reduces to finding the Lagrangian containing only half of the fields. The same
construction takes places for arbitrary integer spin field as well. Further
working in terms of separated variables, we build Lagrangian for arbitrary
integer spin and write it in terms of gauge-invariant objects. Also, we
demonstrate how to restore the full set of variables, thus receiving Lagrangian
for the massive fields of arbitrary spin in the terms of initial fields.
