The availability of natural uranium has a direct impact on the global capability to sustain the demand from nuclear power plants in the coming decades. Therefore, the expansion scenarios of nuclear power should be analysed in conjunction with long-term dynamics of the uranium market. This paper presents three forms of a partial-equilibrium model of the uranium market. All forms consider global demand as exogenous (input scenarios from the literature) and regional estimates of the quantities and the costs of ultimate resources (results obtained from previous work). The three forms differ by the market constraints and the market structure considered. Comparing them highlights the role of the market structure and the impact of some key parameters of the market dynamics on the long-term availability of uranium. An important finding is the influence of two constraints: the anticipation of demand and the significant role played by the correlation between price and exploration expenses in shaping the price trends. In addition, results from simulations highlight different long-term dynamics when the producers are allocated into a limited number of regions (to simulate an oligopoly) compared to a single region (undefined number of players to simulate perfect competition).