Behçet's Disease (BD) is a multi-systemic, auto-inflammatory disorder that is characterized by recurrent episodes of inflammatory manifestations affecting skin, mucosa, eyes, blood vessels, joints and several other organs. BD is classified as a multifactorial disease with an important contribution of genetics. Genetic studies suggest that there is a strong association of BD with a Class I major histocompatibility complex antigen, named HLA-B*51, along with several other weaker associations with genes encoding proteins involved in inflammation. However, pathogenic mechanisms associated with these genetic variations and their interactions with the environment have not been elucidated yet. In this paper, we present a mathematical model for BD based on a dynamical systems perspective that captures especially the relapsing nature of the disease. We propose a disease progression mechanism and construct a model, in the form of coupled ordinary differential equations (ODEs), which reveals the occurrence pattern of the disease in the population. According to our model, the disease has three distinct modes describing different phenotypes of people carrying HLA-B*51 tissue antigen, namely, the Healthy Carrier, the Potential Patient and the Active Patient. We herein present an exemplary mathematical model for BD, for the first time in the literature, that concisely captures the actions of many cell types together with genetic and environmental effects. The proposed model provides insight into this complex inflammatory disease which may lead to identification of new tools for its treatment and prevention.