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The shapes of isolated Bok globules and embedded dense cores of molecularclouds are analyzed using a nonparametric method, under the alternatehypotheses that they are randomly oriented prolate objects or that they arerandomly oriented oblate objects. In all cases, the prolate hypothesis gives abetter fit to the data. If Bok globules are oblate, they must be very flat; theaverage axis ratio is b/a = 0.3, and few or no globules can have b/a > 0.7. IfBok globules are prolate, then the mean axis ratio is b/a = 0.5. For most datasamples of dense cores, the randomly-oriented oblate hypothesis can be rejectedat the 99% confidence level. If the dense cores are prolate, their mean axisratio is approximately 0.4 to 0.5. Dense cores are significantly different inshape from the clouds in which they are embedded; clouds have flatter apparentshapes, and are inconsistent with a population of randomly orientedaxisymmetric objects.Comment: 26 pages (LaTeX) including 8 postscript figures; to appear in Ap

The Shapes of Dense Cores and Bok Globules