AbstractSmall‐amplitude standing oscillations of a fluid in a basin of parabolic bottom profile, but of such aspect ratio that the shallow‐water approximation is not valid, are examined. The eigenvalue problem determining the periods of the waves is solved using Frobenius series representations of the solutions in conjunction with the requirement that these be bounded. When this approach fails for large values of the aspect ratio, recourse is taken to a perturbation expansion of the problem. Finally the results of laboratory experiments are found to agree well with the predicti