Multibeam bathymetric data is modeled from a Bayesian ''smoothness priors'' framework. Smoothness priors is a penalized likelihood-nonparametric linear regression form of modeling and the bathymetry data are modeled one beam at-a-time. The method is applied to data previously analyzed in Goff and Jordan (1988) and Gilbert and Malinverno (1988). The results contrast nonparametric and parametric modeling, dispute the almost conventional removal of ''deterministic'' components prior to stochastic modeling and reveal new evidence about mid-ocean ridge spreading processes. ¿ American Geophysical Union 1990