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The Smith-Watson-Topper (SWT) parameter was originally suggested and is still widely used to account for a mean stress in fatigue life analysis. It is well recognized however, that the SWT parameter might be non-conservative for cyclic loads that involve relatively large compressive mean stresses. A new energy interpretation of the SWT parameter is proposed. This interpretation is formulated in terms of the sum of strain energy density, the complementary strain energy density supplemented by the strain energy density associated with a mean stress in the cycle. Then, a new deviatoric formulation of the SWTD parameter is proposed. Capability of the deviatoric SWTD parameter to correlate experimental data for 7075-T651Al and ASTM A723 steel under various positive and negative mean stresses is presented. At high negative mean stresses, the deviatoric SWTD parameter demonstrates a fairly good correlation where the original SWT parameter is unable to correlate the data.