Cities are the drivers of socioeconomic innovation and are also forced to address the accelerating risk of failure in providing essential services such as water supply today and in the future. Here, we investigate the resilience of urban water supply security, which is defined in terms of the services that citizens receive. The resilience of services is determined by the availability and robustness of critical system elements or “capitals” (water resources, infrastructure, finances, management efficacy, and community adaptation). We translate quantitative information about this portfolio of capitals from seven contrasting cities on four continents into parameters of a coupled system dynamics model. Water services are disrupted by recurring stochastic shocks, and we simulate the dynamics of impact and recovery cycles. Resilience emerges under various constraints, expressed in terms of each city's capital portfolio. Systematic assessment of the parameter space produces the urban water resilience landscape, and we determine the position of each city along a continuous gradient from water insecure and nonresilient to secure and resilient systems. In several cities stochastic disturbance regimes challenge steady‐state conditions and drive system collapse. While water insecure and nonresilient cities risk being pushed into a poverty trap, cities which have developed excess capitals risk being trapped in rigidity and crossing a tipping point from high to low services and collapse. Where public services are insufficient, community adaptation improves water security and resilience to varying degrees. Our results highlight the need for resilience thinking in the governance of urban water systems under global change pressures.