An experimental researeh is presented for a low carbon steel using test pieces with fillets under combination of alternating uniaxiall stress σ_a (amplitude) and tensile mean stress σ_m. The aim of this presentation is to establish the criterion when the maximum stress exceed the yield stress and reach the tensile strength. Results are following : The criterion appears to be a constant or rather increasing slope to the σ_m axis within the yielding zone of maximum stress and then drops linearly to the point of tensile strength on the σ_m axis when it reaches the tensile strength of the material.