We calculate the transverse momentum $p_T$ distribution for production
of the $\Upsilon$ states in hadronic reactions. For small $p_T (\leq 
M_\Upsilon)$, we resum to all orders in the strong coupling $\alpha_s$
the process-independent large logarithmic contributions that arise from 
initial-state gluon showers. We demonstrate that the $p_T$ distribution
at low $p_T$ is dominated by the region of small impact parameter $b$ and 
that it may be computed reliably in perturbative theory. We express the 
cross section at large $p_T4 by the ${\cal O}(\alpha_s^3)$ lowest-order 
non-vanishing perturbative contribution. Our results are consistent with
data from the Fermilab Tevatron collider.