Rubber-like polymers are widely used in various engineering applications. One of the recent trends in the marine energy industry is the use a flexible membranes to convert wave energy to useful mechanical energy. Such devices operate in harsh corrosive environment making them crucial to predict their long-term performance, especially in fatigue. Hence, research presented introduces a phase field model for fracture of rubber-like polymers. The growing interest in phase field models based on variational formulations can be attributed to the recent advancements in computing power, facilitating the efficient resolution of complex problems. Notably, Miehe et al. [1] proposed a phase field model for finite strain, incorporating a micro-mechanically motivated constitutive model for rubber-like materials. This was later extended to include viscoelasticity by Loew et al. [2]. Despite subsequent studies by many, there is a limited exploration of phase field modelling for incompressible materials especially for fatigue modelling. This paper addresses this gap by presenting a phase field formulation tailored for incompressible materials. A mixed displacement-pressure formulation, accommodating quasi-incompressibility, is coupled with a second-order approximation of the phase field. However, the incompressibility constraint is relaxed in the region of material degradation to facilitate smooth crack propagation. The standard approach involves crack propagation governed by Griffith's energy release rate, wherein a diffused crack field over a volume, approximates a surface crack. The study employs a quadratic degradation function, and a staggered scheme is implemented to solve the coupled problem. An adaptive time-stepping scheme is used to enhance the algorithmic efficiency. The finite element formulation is executed in ABAQUS through a user element subroutine (UEL). The effectiveness of the algorithm is demonstrated through 2D and 3D numerical examples. Finally, the developed algorithm is employed to investigate the influence of damage on various types of flexible wave energy converters.