In this paper, we propose a new framework for the study of cellular networks called the fluid model and we derive from this model analytical formulas for interference, outage probability, and spatial outage probability. The key idea of the fluid model is to consider the discrete base stations (BS) entities as a continuum of transmitters which are spatially distributed in the network. This allows us to obtain simple analytical expressions of the main characteristics of the network. In this paper, we focus on CDMA systems. This approach is however also applicable to other technologies like OFDMA. A closed-form formula of the downlink other-cell interference factor, f, is provided and compared to simulations performed in a traditional hexagonal network. From f, we are able to derive the global outage probability and the spatial outage probability, which depends on the location of a mobile station (MS) initiating a new call.