In this paper we develop an algorithm for assessing the effect of small perturbations of the data on the validity of a postulated generalized linear model.The procedure is based on the geometric notion of shape operator, a single mathematical object that gathers together all the normal curvatures of a given influence graph or hypersurface.In addition to introducing relevant theoretical notions and explaining the foundations of the local influence assessment method in a generalized linear model with a canonical link, we provide a detailed example of application together with the explicit R code implementing the algorithm.