A search for long-lived charged massive particles in CDF's Run1b
data sample is presented.  The search looks for highly ionizing tracks which
would result from slowly moving massive particles.  We search for strongly
produced particles using a stable color triplet quark as a reference model,
and a separate search was performed for weakly produced particles using
long-lived sleptons in Gauge-Mediated Supersymmetry Breaking as a reference
model.  No excess over background was observed, and we derive limits on the
cross-sections for production of these particles.  Prospects for RunII are
also discussed.