The application of the selective laser melting (SLM) method requires knowledge of not only the properties of the material after manufacturing, but also after mechanical loading. The aim of this work is to investigate the strain-rate dependence and microstructure of Ti6Al4V samples manufactured by SLM method with different angles to the building platform. SLM Ti-6Al-4V samples were manufactured using the EOSINT M280 (EOS GmbH) at angles of 0°, 30°, 45°, 90° to the building platform. A medicine Ti6Al4V (ASTM grade 23) powder was used for the study. Tensile tests were performed with an Instron test machine using two strain rates 0.5 mm/min and 2 mm/min at room temperature. It was found the strain-rate dependence in the studied samples. The features of the mechanisms of hardening and softening in an investigated SLM Ti-6Al-V alloy are discussed.