Low urinary tract dysfunctions and symptoms (LUTS) and Urinary incontinence (UI) in particular is a medical condition that affects millions of people worldwide. One of the most promising long term treatments for this condition is the use of an artificial urinary sphincter (AUS). The AUS is a medical device that is implanted around the urethra to provide continence control by constricting the later. Understanding the biomechanics and in particular the mechanical properties of the urethra is a critical prerequisite for designing an effective AUS to treat urinary incontinence. However, performing Tests on human urethras presents significant challenges due to ethical considerations and the limited availability of human tissue samples. As a result, animal testing has been performed to study the mechanical properties of the urethra. Among various candidates, pig urethras have similar dimensions, anatomical features, and tissue properties to human urethras, making them a suitable replacement for studying the mechanical properties of the human urethra. Furthermore, pig urethras can be obtained from a readily available and sustainable source, allowing for more extensive testing and experimentation. In this paper, experimental results from mechanical pressure tests on pig urethra are presented and compared with human urethra. Then non linear constitutive models are proposed to fit with our experimental values. Due to its close fit to our experimental data, the model of Fung has been selected as a future reference in order to perform simulations on several urethra geometries and analyse those data to accurately design our Artificial Urinary Sphincter.