AbstractAlthough river meanders are not perfectly regular their serial statistics show periodic tendencies which cannot be explained by previous stochastic models. The regular and random approaches to meander geometry can be reconciled in a disturbed periodic model with separate scale, sinuosity, and irregularity parameters. Meandering is viewed as a deterministic oscillation but irregularity is introduced by quasi‐random variability in valley‐floor topography and materials. For stability such a model needs either a Bagnold type limit on bend curvature or frictional damping of the oscillatory response to individual disturbances. Realistic statistical properties are derived for the second case. The differential equation for direction can be approximated by a second‐order autoregression, which generates realistic simulated patterns and gives a good fit to natural direction series.