Abstract Motivation The shape of a cell is tightly controlled, and reflects important processes including actomyosin activity, adhesion properties, cell differentiation, and polarization. Hence, it is informative to link cell shape to genetic and other perturbations. However, most currently used cell shape descriptors capture only simple geometric features such as volume and sphericity. We propose FlowShape, a new framework to study cell shapes in a complete and generic way. Results In our framework a cell shape is represented by measuring the curvature of the shape and mapping it onto a sphere in a conformal manner. This single function on the sphere is next approximated by a series expansion: the spherical harmonics decomposition. The decomposition facilitates many analyses, including shape alignment and statistical cell shape comparison. The new tool is applied to perform a complete, generic analysis of cell shapes, using the early Caenorhabditis elegans embryo as a model case. We distinguish and characterize the cells at the seven-cell stage. Next, a filter is designed to identify protrusions on the cell shape to highlight lamellipodia in cells. Further, the framework is used to identify any shape changes following a gene knockdown of the Wnt pathway. Cells are first optimally aligned using the fast Fourier transform, followed by calculating an average shape. Shape differences between conditions are next quantified and compared to an empirical distribution. Finally, we put forward a highly performant implementation of the core algorithm, as well as routines to characterize, align and compare cell shapes, through the open-source software package FlowShape. Availability and implementation The data and code needed to recreate the results are freely available at https://doi.org/10.5281/zenodo.7778752. The most recent version of the software is maintained at https://bitbucket.org/pgmsembryogenesis/flowshape/.