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Naturalness bounds on weak scale supersymmetry in the context of radiativebreaking of the electro-weak symmetry are analyzed. In the case of minimalsupergravity it is found that for low tan\beta and for low values of finetuning Phi, where Phi is defined essentially by the ratio \mu^2/M_Z^2 where \muis the Higgs mixing parameter and M_Z is the Z boson mass, the allowed valuesof the universal scalar parameter m_0, and the universal gaugino mass m_{1/2}lie on the surface of an ellipsoid with radii fixed by \Phi leading to tightlyconstrained upper bounds \sim \sqrt\Phi.Thus for tan\beta\leq 2(\leq 5) it isfound that the upper limits for the entire set of sparticle masses lie in therange < 700 GeV (<1.5TeV) for any reasonable range of fine tuning (\Phi\leq20). However, it is found that there exist regions of the parameter space wherethe fine tuning does not tightly constrain m_0 and m_{1/2}. Effects of non-universalities in the Higgs sector and in the third generation sector onnaturalness bounds are also analyzed and it is found that non-universalitiescan significantly affect the upper bounds. It is also found that achieving themaximum Higgs mass allowed in supergravity unified models requires a highdegree of fine tuning. Thus a heavy sparticle spectrum is indicated if theHiggs mass exceeds 120 GeV. The prospect for the discovery of supersymmetry atthe Tevatron and at the LHC in view of these results is discussed.Comment: 32 pages LaTex. Revised version to appear in Phys.Rev.

Naturalness, weak scale supersymmetry, and the prospect for the observation of supersymmetry at the Fermilab Tevatron and at the CERN LHC