This paper presents a simple model for tsunami sedimentation that can be applied to calculate tsunami flow speed from the thickness and grain size of a tsunami deposit (the inverse problem). For sandy tsunami deposits where grain size and thickness vary gradually in the direction of transport, tsunami sediment transport is modeled as a steady, spatially uniform process. The amount of sediment in suspension is assumed to be in equilibrium with the steady portion of the long period, slowing varying uprush portion of the tsunami. Spatial flow deceleration is assumed to be small and not to contribute significantly to the tsunami deposit. Tsunami deposits are formed from sediment settling from the water column when flow speeds on land go to zero everywhere at the time of maximum tsunami inundation. There is little erosion of the deposit by return flow because it is a slow flow and is concentrated in topographic lows. Variations in grain size of the deposit are found to have more effect on calculated tsunami flow speed than deposit thickness. The model is tested using field data collected at Arop, Papua New Guinea soon after the 1998 tsunami. Speed estimates of 14 m/s at 200 m inland from the shoreline compare favorably with those from a 1-D inundation model and from application of Bernoulli's principle to water levels on buildings left standing after the tsunami. As evidence that the model is applicable to some sandy tsunami deposits, the model reproduces the observed normal grading and vertical variation in sorting and skewness of a deposit formed by the 1998 tsunami.