  Recently, it has been observed that a certain class of classical theories
with constraints can be quantized by a mathematical procedure known as Rieffel
induction. After a short exposition of this idea, we apply the new quantization
theory to the Stueckelberg-Kibble model. We explicitly construct the physical
state space ${\cal H}_{phys}$, which carries a massive representation of the
Poincar\'e group. The longitudinal one-particle component arises from a
particular Bogoliubov transformation of the five (unphysical) degrees of
freedom one has started with. Our discussion exhibits the particular features
of the proposed constrained quantization theory in great clarity.
