We used spaceborne laser altimetry data from the ICESat and ICESat-2 missions to obtain ice elevation and mass change rates between 2003-2008 and 2019 over Svalbard. Elevation changes are derived at orbit crossover locations throughout the study area for glaciated and non-glaciated regions. We provide regional filtered crossover data for both surface types as point shapefiles in EPSG 4326 projection. Data is split into a north-western, north-eastern, and southern region in Spitsbergen in addition to measurements for the islands Barentsoya/Edgeoya and Kvitoya, the ice caps of Austfonna and Vestfonna, and seperate acquisitions over the Storisstraumen Glacier (Basin-3) in Austfonna (only glaciated). Data over icefree regions is not available for Kvitoya. Attribute field specifications are as follows: 'dhdt' is the annual elevation change rate in meters per year, 'dh_elv' is the total elevation change in meters, 'dt_year' is the timespan between ICESat and ICESat-2 acquisitions in decimal years, 'elv_IS2' is the interpolated ICESat-2 height value from the two nearest measurements to the crossing position in meters, 'elv_IS' is the interpolated ICESat height value from the two nearest measurements to the crossing position in meters, 'year_IS2' is the interpolated time from the two nearest measurements to the crossing location in decimal years, and 'year_IS' is the interpolated time in decimal years from the two nearest measurements to the crossing location in decimal years.