To search for a single parameter to evaluate the stress state in rail head during wheel/rail rolling contact situations, the stress-based and the strain based phenomenological approaches for multiaxial fatigue analysis can be considered as the candidates. Following the stress-based approach, the maximum von Mises stress range can be applied as a single parameter to evaluate the stress state in the rail head. However, the von Mises stress range only relies on the stress field in the rail head for the fatigue analysis, which is not sufficient for assessing the fatigue resistance of the rail steel. The Smith-Watson-Topper (SWT) method, the strain-based phenomenological approach for multiaxial fatigue analysis which considers stress, elastic strain and plastic strain components, is then adopted to study rolling contact fatigue in the rail head. Combining with the three-dimensional finite element modelling of a steady-state wheel/rail rolling contact, the numerical procedure to calculate the SWT parameter in the rail head is presented. The capability of the SWT method to predict the initiation of fatigue cracks in the rail head is confirmed in a case study. Consequently, the maximum SWT parameter is proposed as a single parameter to effectively evaluate the stress state in the rail head.