Highway traffic flows are generally modeled by partial differential equations (PDEs). These models are used by traffic engineers for road design, planning or management. However, they often fail to capture important features of empirical traffic flow studies, particularly at small scales. In this talk, I will propose a fairly simple stochastic model for highway traffic flows in the form of a nonlinear stochastic partial differential equation (SPDE) with random coefficients driven by a Poisson random measure. I will discuss the well posedness of the proposed equation as well as the corresponding inverse problem that I will illustrate by its calibration to high resolution traffic data from highway 101 in Los Angeles. I will also present a more sophisticated spde in the form of a system of coupled hyperbolic-parabolic equations.