This work is an experimental study of the motion and deformation of a bioartificial capsule flowing in a tube of 4 mm diameter. The capsules, initially designed for medical applications, are droplets of salt water surrounded by a thin polymeric membrane. They are immersed in a very viscous Newtonian silicone oil that flows through a tube in the Stokes regime. The properties of the capsules were carefully determined. Two previous experimental papers were devoted to their characterization by osmotic swelling and compression between two plates. The present work also provides a series of tests that allows an accurate definition of the experimental model under investigation. The capsules are buoyant and initially quasi-spherical. Nevertheless, buoyancy and small departures from sphericity are shown to have no significant effects, provided the flowing velocity is large enough for the viscous stress to become predominant. The capsules are also initially slightly over-inflated, but there is no mass transfer through the membrane during the present experiments. Their volume therefore remains constant. The membrane can be described as an elastic two-dimensional material, the elastic moduli of which are independent of the deformation. Far from the tube ends, the capsule reaches a steady state that depends on two parameters: the capillary number, $\hbox{\it Ca}$; and the ratio of the radius of the capsule to that of the tube, $a/R$. The capillary number, which compares the hydrodynamic stresses to the elastic tensions in the membrane, was varied between 0 and 0.125. The radius ratio, which measures the magnitude of the confinement, was varied from 0.75 to 0.95. In the range investigated, the membrane material always remains in the elastic domain. At fixed $a/R$, the capsule is stretched in the axial direction when $\hbox{\it Ca}$ is increased. The process of deformation involves two main stages. At small to moderate $\hbox{\it Ca}$, the lateral dimension of the capsule decreases whereas its axial length increases. The capsule is rounded at both ends, but the curvature of its rear decreases as $\hbox{\it Ca}$ increases. At large $\hbox{\it Ca}$, the rear buckles inward. Then, the negative rear curvature goes on decreasing whereas the lateral dimension of the capsule reaches a constant value. On the other hand, increasing $a/R$ promotes the deformation: the process remains qualitatively the same, but the different stages are attained for smaller values of $\hbox{\it Ca}$. Comparisons with available numerical simulations show that the results are strongly dependent on the properties of the capsules.