This dataset provides the research data and software for the publication: M. Fricke, E. Ouro-Koura, S. Raju, R. von Klitzing, J. De Coninck, D. Bothe: An analytical study of capillary rise dynamics: Critical conditions and hidden oscillations which was published in the Journal Physica D: Nonlinear Phenomena. The experimental data for the capillary rise of silicon oil, ethanol and ether has been extracted from the publication D. Quéré: Inertial capillarity, EPL 39 533, DOI:10.1209/epl/i1997-00389-2 (1997) using image analysis methods. It is stored in the csv files Silicon_Oil_Quere1997, Ethanol_Quere1997.csv and Ether_Quere1997. Please use the Python scripts silicon-oil.py, ethanol.py and ether.py to solve the ordinary differential equation model and to generate the plots presented in our publication. The Python library matplotlib was used for plotting. A simple explicit Euler scheme proved sufficient to solve the ordinary differential equation in its dimensionless form. It is implemented in the file capRiseOdeSolver.py.