Traditional morphometric method measures the linear distance between two points on the body surface. Statistical techniques, mainly covariance analysis and principle component analysis, are respectively used in single- and multi- variable statistical inferences. Their purpose is to overcome the bias due to allometric growth. Geomorphometric methods (mainly superimposition method) studied the size and shape of organisms was developed at recent decade. These methods not only measure and analyze body shape and size directly, but are immune to the disturbance of allometric growth. They also enable scientists to study organic structure on a three dimensional space. In this study, coordinates of landmarks on beaks surface were recorded to give information of shape as well as caliper distances. Superimposition method (Procrustes residuals) was applied to examine the difference between sexes, local populations and among different species of octopus. And the phenograms based on caliper distance and superimposition method were compared with the hypothesis of Norman and Sweeney on Octopus phylogeny. Samples of all 11 species of octopus, belonging to genus Cistopus and three species-group of genus Octopus were collected around the water of Taiwan. No significant differences on landmark shape between sexes of O. aegina and of O. marginatus were found through principal component analysis. Samples of O. marginatus from Tungkang and Dahsi could be discriminated through the first principal component. The result does not match with that from DNA sequence analysis already reported. Such conflicts were considered the result of environmental effects. Canonical discrimination method was used for two types of data, namely Procrustes residuals and caliper distances. All species were significantly different from each other. A discriminate function based on Procrustes residuals data reclassified 92.7% of the specimens correctly, incomparing to the 86.1% based on caliper distances. Phenogram constructed from a matrix of Mahalanobis distance (D2) also showed different result. It was concluded that: 1) Result of geomorphometric analysis based on landmark data is not compatible with the hypothesis of Norman and Sweeny. 2) Beak characters based on caliper distance are suitable for discrimination between genera or species-groups, and support the separation of O. luteus from O. minor and O. sp. TW35. Our study suggests that, either traditional morphometric method or the new geomorphometric method is a better tool for showing environmental effects than for phylognetic studies.