The 1975 May 26 earthquake, of magnitude Ms = 7.9, occurred in the North Atlantic close to the Azores Archipelago. Its epicentre, as given by US Geological Survey, was 17.5° W, 35.9° N, 200 km south of the Gloria Fault. Several authors determined the focal mechanism as a dextral strike-slip event with no significant dip-slip component, compatible with the relative motion between Eurasia and Nubia plates but away from the presumed plate boundary. The 1975 earthquake generated a tsunami of small amplitude, recorded at the Portuguese tide-gauge network, in Spain and Northern Africa. The peculiar location of the earthquake and tsunami source and the generation of a noticeable tsunami were already discussed by several authors, but up to now, no direct modelling of the tsunami generation and propagation was made to judge the set of source solutions obtained by seismological analysis. In this paper, we present tsunami simulations, backward ray tracing and forward non-linear shallow water simulations using data from Iberia and Azores and Northern Africa. We show that a good fit between observed data and synthetic waveforms can be obtained with a focal mechanism with no significant dip-slip component, favouring its interpretation as almost pure dextral strike-slip event located in an old fracture zone south of Gloria Fault. ©2008 Springer Science+Business Media B.V.