A macroscopic loading model applicable to time-dependent and congested pedestrian flows in public walking areas is proposed. Building on the continuum theory of pedestrian flows and the cell transmission model for car traffic, an isotropic framework is developed that can describe the simultaneous and potentially conflicting propagation of multiple pedestrian groups. The model is formulated at the aggregate level and thus computationally cheap, which is advantageous for studying large-scale problems. A detailed analysis of several basic flow patterns including counter- and cross flows, as well as two generic scenarios involving a corner- and a bottleneck flow is carried out. Various behavioral patterns ranging from disciplined queueing to impatient jostling can be realistically reproduced. Following a systematic model calibration, two case studies involving a Swiss railway station and a Dutch bottleneck flow experiment are presented. A comparison with the social force model and pedestrian tracking data shows a good performance of the proposed model with respect to predictions of travel time and density.