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Force and moment characteristics of pneumatic tyres play a vital role in the effective and efficient vehicle handling behaviour. Prediction of these transient characteristics during vehicle cornering behaviour using finite element techniques is a complex dynamic problem involving geometrical non-linearity, material non-linearity and boundary non-linearity. In addition, tyre materials are incompressible and are embedded with reinforcements, making them composite in nature. In the present study, three finite element techniques viz., Implicit Lagrangian Method, Implicit Mixed Lagrangian Eulerian Method and Explicit Lagrangian Method are used to simulate the dynamic cornering behaviour of a passenger car radial tyre. ABAQUS/Standard and ABAQUS/Explicit, popular general-purpose non-linear finite element codes, are used to simulate the cornering response at various loading and operating conditions.