Abstract Airborne laser scanning (ALS) data are not usually considered to be very informative with respect to tree species, and this information is often obtained by combining such data with spectral image material. The aim here was to test the ability of variables derived solely from ALS data to describe the crown shape and structure characteristics required for tree species discrimination. For that purpose, we constructed tree crown approximations from the three-dimensional return data by applying a computational geometry approach, the alpha shape concept, and developed metrics for describing them. We examined the ability of these metrics to classify Scandinavian commercial species (pine, spruce, and deciduous trees) by means of linear discriminant analysis and compared the alpha shape metrics with groups of ALS-based height, density, intensity, and two-dimensional texture variables. For evaluating the classification accuracy, we used a test data set composed of 92 dominant or codominant trees detected and delineated manually from ALS data with a density of approximately 40 returns m−2. The alpha shape metrics proved capable of discriminating between all three species classes evaluated, and several height distribution and texture variables were found to discriminate between the coniferous tree species. An overall accuracy of approximately 95% and a κ coefficient of 0.90 was achieved using a combination of the variables. Because this initial application of the alpha shape metrics was carried out using a test data set on only such trees that are clearly detectable from remotely sensed data, further research is required to apply the approach presented here within stands with a continuous canopy. Furthermore, as the tree observations considered here were highly biased toward mature coniferous trees, experiments using more representative data sets are needed to generalize the result obtained.