The recently approved COBRAS/SAMBA cosmic microwave background mission will also have a major impact on measurements of the Sunyaev-Zeldovich effect. The frequency of three of the channels (150 GHz, 217 GHz, 353 GHz) are chosen to optimize measurements of the thermal and kinetic SZ effect mainly caused by hot gas in clusters of galaxies. Estimates of the number of detected clusters are somewhat uncertain due to incomplete knowledge of the gas mass function of clusters and the distribution of hot gas at large radii. Straightforward interpolation of X-ray observations of the 200 X-ray brightest clusters gives a firm lower limit of approximately 3000 detected clusters of which roughly half should be resolved. If the gas distribution of clusters should turn out to be favourable and/or the cluster evolution with redshift is weak, this number could be higher by a factor of up to ten. Using an optimal filtering technique a measurement of the bulk peculiar velocity of a sample of about 200 of the resolved clusters will be possible with a 1-sigma error of 100 - 200 km/s.