We report on a search for supersymmetric squark and gluino
particles in a data sample of 19 pb^-1 of ppbar collisions at sqrt s = 1.8
TeV recorded by the Collider Detector at Fermilab.  We searched for events
containing jets plus appreciable missing transverse energy (missing E_T).
This signature is indicative of pair production and subsequent decay of
squarks and/or gluinos.  After all cuts, there are 18 events with missing
E_T > 60 GeV and three jets, and 6 events with missing E_T > 60 GeV and four
jets.  These numbers of events are consistent with estimates of standard model
processes plus detector-induced background sources.  The analysis yields lower
limits on gluino and squark masses, based on the predictions from the minimal
supersymmetric extension of the standard model.  At the 95% confidence level,
we find gluino and squark mass limits up to 216 GeV/c^2, assuming equal gluino
and squark masses, and gluino mass limits up to 173 GeV/c^2, independent of
squark mass.