Current artificial heart valves either have limited lifespan or require the recipient to be on permanent anticoagulation therapy. In this paper, effort is made to assess a newly developed bileaflet valve prosthesis made of synthetic flexible leaflet materials, whose geometry and material properties are based on those of the native mitral valve, with a view to providing superior options for mitral valve replacement. Computational analysis is employed to evaluate the geometric and material design of the valve, by investigation of its mechanical behaviour and unsteady flow characteristics. The immersed boundary (IB) method is used for the dynamic modelling of the large deformation of the valve leaflets and the fluid-structure interactions. The IB simulation is first validated for the aortic prosthesis subjected to a hydrostatic loading. The predicted displacement fields by IB are compared with those obtained using ANSYS, as well as with experimental measurements. Good quantitative agreement is obtained. Moreover, known failure regions of aortic prostheses are identified. The dynamic behaviour of the valve designs is then simulated under four physiological pulsatile flows. Experimental pressure gradients for opening and closure of the valves are in good agreement with IB predictions for all flow rates for both aortic and mitral designs. Importantly, the simulations predicted improved physiological haemodynamics for the novel mitral design. Limitation of the current IB model is also discussed. We conclude that the IB model can be developed to be an extremely effective dynamic simulation tool to aid prosthesis design.