In this thesis, bubble deformation and breakup is investigated for a laminar flow configuration. Viscous forces result in a shear-rate-induced stress acting on the bubble and yielding deformation. Flow of an established hydraulic oil in a joining, cross-flow-type T-junction geometry was studied featuring moderate Reynolds numbers and dilute, dispersed bubbles with a diameter of approximately 0.5 mm. The experimental facility is presented including bubble generation and injection. Optical measurement techniques, including the high-speed shadowgraphy method, are used to measure both single-phase and multiphase flow. The flow pattern of the single-phase configuration is discussed and indications for flow instabilities are found. In the present work, a new model for bubble deformation under dynamic load is introduced in the form of an ordinary differential equation for the deformation energy. Breakup is identified with a critical value of the deformation. The deformation resulting from the proposed model is then compared with the measured deformation of exemplary bubble trajectories. Various errors arising from the measurement arrangement and the model assumptions are discussed and suggestions are stated to improve the model for deformation and breakup.