Compactness, long term stability and no free-space alignment are important advantages of fiber lasers over bulky systems. These fiber lasers have also demonstrated their capability to deliver high-power pulses and are thus suitable for numerous applications. Nevertheless the intensity profile delivered usually has a Gaussian-like shape, which most of the time is sufficient, but it could be interesting, for many applications (laser-biological tissues interactions, heat treatment, industrial laser processing or for seeding large-scale laser facilities like Laser MegaJoule) to obtain a homogeneous intensity profile at the fiber laser output. Moreover several of these applications required a linearly polarized output beam. In order to achieve all these requirements we have developed and realized a new fiber design. This fiber is the first polarization maintaining single-mode fiber delivering a flat top intensity. A high quality flat mode was obtained at 1.05μm through the use of a well-tailored index profile and single-mode behavior was verified by shifting the injection and using the S² imaging. Moreover, boron Stress Applying Parts (SAPs) including in the cladding led to a birefringence of 0.6x10-4 and a measured PER better than 20dB even for a long fiber length (~20 m). Alongside the fabrication, we developed a simulation code, using Comsol Multiphysics®, to take into account the stress dependency induced by the SAPs. Further modeling allows us to present an effectively single-mode fiber design, delivering a top-hat mode profile and exhibiting a polarizing behavior.