One of the well-known models of biochemical networks is the Goodwin model. The model describes an oscillatory behavior in an enzymatic control process which is expressed in a set of nonlinear ordinary differential equations and is often associated with biochemical experiments containing uncertainties in data measurements. These uncertainties are possibly either due to limitations of available data, complexity of the networks, or environmental or demographic changes. In view of these possible uncertainties, in this paper we shall study solutions of the Goodwin model that is considered as a fuzzy initial value problem. Three types of fuzzy differential solutions are discussed: Hukuhara differential and its generalization, and fuzzy differential inclusions. Applications of fuzzy arithmetic to those types lead into the alpha-cut deterministic systems, which are then solved by the Runge-Kutta method. Among those three types, the fuzzy differential inclusions is able to capture oscillatory behavior as the Goodwin model should have. Taking the benefit from the fuzzy differential inclusions method, we then demonstrate how to estimate parameters of the model when uncertainty gets involved in the equation. As an illustration, we apply the method to our generated fuzzy simulation data and calculate parameters using nonlinear least square method. Keywords: Fuzzy initial value problems, fuzzy arithmetic, alpha-cut deterministic systems, Hukuhara differential, generalized Hukuhara differential, fuzzy differential inclusions.