The tolerance to shear stress of Tetraselmis suecica, Isochrysis galbana, Skeletonema costatum, and Chaetoceros muelleri was determined in shear cylinders. The shear tolerance of the microalgae species strongly depends on the strain. I. galbana, S. costatum, and C. muelleri exposed to shear stress between 1.2 and 5.4 Pa resulted in severe cell damage. T. suecica is not sensitive to stresses up to 80 Pa. The possibility to grow these algae in a tubular photobioreactor (PBR) using a centrifugal pump for recirculation of the algae suspension was studied. The shear stresses imposed on the algae in the circulation tubes and at the pressure side of the pump were 0.57 and 1.82 Pa, respectively. The shear stress tolerant T. suecica was successfully cultivated in the PBR. Growth of I. galbana, S. costatum, and C. muelleri in the tubular PBR was not observed, not even at the lowest pumping speed. For the latter shear sensitive strains, the encountered shear stress levels were in the order of magnitude of the determined maximum shear tolerance of the algae. An equation was used to simulate the effect of possible damage of microalgae caused by passages through local high shear zones in centrifugal pumps on the total algae culture in the PBR. This simulation shows that a culture of shear stress sensitive species is bound to collapse after only limited number of passages, confirming the importance of considering shear stress as a process parameter in future design of closed PBRs for microalgal cultivation.