This paper presents a study on the pressure transient behaviour during the injection period in a vertical well in the presence of wellbore storage and skin effect. The two-phase water-oil radial flow problem is solved using a semi-analytical technique called the Laplace-Transform Finite-Difference method. Moreover, the factors that influence the degree of wellbore storage and skin effect are analysed. The results demonstrated that the effect of wellbore storage on the pressure transient behaviour is significant during the early times. Factors such as compressibility of fluid, effective wellbore volume and endpoint mobility ratio significantly affect the duration of wellbore storage. The impact of the skin during the injection period is significant on the pressure transient behaviour and could last for a longer duration. A substantial effect of skin is observed for a positive skin factor and unfavourable endpoint mobility ratio. In addition, the duration of the effect is directly proportional to the thickness of the skin zone. Hence attention must be given to the parameters that could prolong these effects and included in the solution methods to precisely interpret the injection period pressure transient behaviour for a better estimation of the reservoir and well properties. © The Authors 2020.