SUMMARY We report on the analysis of M2 ocean tide loading (OTL) kinematic GPS vertical displacement and tidal gravity measurements using 26 GPS and four gravimetric sites across the Canary Islands archipelago. In this region, the standard deviation among recent ocean tide models is lower than 0.4 cm in amplitude and 0.3° in phase, which are suitably accurate for displacement modelling. However, for gravity we need to model regional ocean tides to achieve enough accuracy in the loading calculations. Particularly, this study improves the predicted OTL gravity variations when global ocean models are replaced with the regional model CIAM2 which assimilates local tide gauge data. These small ocean tide model errors allow us to use the differences between observed and predicted OTL values to study the elastic and anelastic properties of the solid Earth around the Canary Islands. In the prediction of OTL, we first used the recent elastic STW105 and S362ANI seismic models, obtaining average observed minus predicted residuals of 1.2–1.3 mm for vertical displacement and 3 nm s−2 for gravity. After the STW105 and S362ANI models were adjusted for anelasticity, by considering a constant quality factor Q at periods ranging from 1 s to 12.42 hr, the average misfit between observations and predicted OTL values reduced to 0.7–0.8 mm for vertical displacement and to 1 nm s−2 for gravity. However, the average vertical displacement misfit is made up from site misfits less than 0.5 mm in western islands but for the easternmost islands of Lanzarote and Fuerteventura, they still reach up to nearly 2 mm at some sites, which still exceeds the uncertainty in the GPS observations. It is hypothesized that mantle upwelling underneath the Canary Islands, creating spatial variations in the elastic properties, causes the large residuals observed in the eastern islands. We reduced the shear modulus by up to 35 per cent in the upper mantle layer of 24.4–220 km depth. This produced residual observed minus model differences of about 0.7 mm for the sites on Lanzarote and Fuerteventura, comparable to the results obtained for the GPS sites across the rest of the archipelago, whose residuals in turn were also slightly reduced through the VS velocity and shear modulus reductions (by 0.2 mm on average).