In this paper, the applicability and performance of linear discriminant analysis (LDA) for building types' classification are investigated. Building models at a level of detail 1 (LoD1) are derived from real estate cadastral building footprints and digital surface models from stereoscopic airborne images. In several experiments for two cities in Germany (Berlin and Munich), we first evaluate the discriminatory power of 26 different shape-based features which describe the physiognomy of individual buildings in terms of 1-D (e.g., length), 2-D (e.g., area), and 3-D (e.g., volume) features. While 1-D features show low contributions to the discrimination of the five building types, we observe high contributions of the 3-D shape index and 2-D measures of compactness. In a second group of experiments, the size of training samples for the classification process is investigated with the outcome that a size of 10% of the total number of labeled features is practicable in terms of size and accuracy. In a third battery of experiments, the selected features and training sample size are used for the classification of building types resulting in kappa values of 0.94 for both cities. In the final experiments, the geographical transfer between the two cities is investigated reaching kappa values of 0.93 and 0.91, respectively. The tests show that a simple linear classifier like LDA can handle building types' classification without much user interaction compared to more complex classification methods but is limited when similar building types (e.g., perimeter block development and block development) are to be discriminated.