A balloon catheter assembly comprises a balloon 44 having attached to or in its wall one or more filar (threadlike) elements 46, extending from one end of the balloon to the other. The filar elements are made of a material which is at least as flexible as the material forming the walls of the balloon. In the event of circular burst of the balloon, the filar element(s) prevent disconnection of the material of the balloon into two or more separate pieces. The filar element(s) become attached to or in the material of the balloon wall when the raw material is inflated to the shape of a mould (figures 57). The filar elements may comprise a natural fibre such as cotton, a synthetic fibre such as paraaramid or PTFE fibre, or a metal wire, with a strength of 420 N. The filar elements may extend parallel to the longitudinal axis 48 of the balloon or may be arranged in a helix.