Data are from two independent experimental campaigns in 3D wave basins, which were conducted to investigate the interaction between surface waves and thin floating plates, mimicking the interaction between ocean waves and sea ice floes. One experiment tested irregular waves, including directional spreading, with two peak steepness values comparable to storm and polar cyclone conditions, interacting with a single square polypropylene floe, with length close to the dominant wavelength (scattering regime) -- data file Single_Plate.zip. The second experiment used arrays of wooden floes with low- and high-concentrations to test wave-floe interaction at a range of peak periods and peak wave steepness spanning from gentle to storm-like conditions -- data file MultipleDisks.zip. Both data files contains raw data, experimental matrix and experimental set. Data are fully described and analysed in a contribution to "Theory, modelling and observations of marginal ice zone dynamics: Multidisciplinary perspectives and outlooks" a special theme issue for Philosophical Transactions A: Toffoli A., Pitt J. P. A., Alberello A., Bennetts L.G., 2022. Modelling attenuation of irregular wave fields by artificial ice floes in the laboratory. Philos. T. Roy. Soc. A (submitted) Additional information on the data sets can be found in Bennetts LG, Alberello A, Meylan MH, Cavaliere C, Babanin AV, Toffoli A. 2015 An idealised experimental model of ocean surface wave transmission by an ice floe, Ocean Model. 96, 85���92 Bennetts LG, Williams TD. 2015 Water wave transmission by an array of floating discs, Proc. Roy. Soc. A 471, 20140698