Deductive molecular mechanics is applied to study the relative stability and mechanical properties of carbon allotropes containing isolated σ-bonds. Our approach demonstrates numerical accuracy comparable to that of density-functional theory, but achieved with dramatically lower computational costs. We also show how the relative stability of carbon allotropes may be explained from a chemical perspective using the concept of strain of bonds (or rings) in close analogy to theoretical organic chemistry. Besides that, the role of nonbonding electrostatic interactions as the key factor causing the differences in mechanical properties (in particular, hardness) of the allotropes is emphasized and discussed. The ADAMAS program developed on the basis of this study fairly reproduces spatial and electronic structure as well as mechanical properties of carbon allotropes.