The ‘relativistic” mass concept is rooted in the problematic longitudinal and transverse mass equations emerging from the Lorentz transformation, as presented by Einstein in his 1905 paper on Special Relativity. These equations, although actual outcomes of the Special Relativity, and verified in this paper through both simplified dimensional analyses and conservation of energy principle, had later been implicitly dropped and replaced by an ad-hoc relativistic mass equation, needed to maintain the consistency of the Special Relativity with the conservation of momentum law—although it results in its violation of the law of conservation of energy. Maintaining the latter law, results in the same transverse mass equation as obtained in Einstein’s said paper. The relativistic mass adopted in the literature is but an attempt to conceal contradictions in the Special Relativity, and a convenient means for arriving at the relativistic kinetic energy formula implying the desired mass-energy equivalence equation E = mc2. In this paper, the incoherence of the Special Relativity emerging from its established mass formulae is revealed through simplified physical demonstrations. Depending on the force definition and the “moving” mass equation used, four different formulae for the relativistic kinetic energy are obtained, all validated from the Special Relativity perspective, creating a detrimental incoherence in the theory. All these formulae are reduced to the classical kinetic energy equation for v << c (v = velocity, c = speed of light). It is revealed that the energy equation E = mc2 is not a valid consequence of the Special Relativity.