Anisotropic mechanical behavior is an inherent characteristic of parts produced using additive manufacturing (AM) techniques in which parts are built layer by layer. It is expected that in-plane and out-of-plane properties be different in these parts. E-beam fabrication is not an exception to this. It is, however, desirable to keep this degree of anisotropy to a minimum level and be able to produce parts with comparable mechanical strength in both in-plane and out-of-plane directions. In this manuscript, this degree of anisotropy is investigated for Ti6Al4V parts produced using this technique through tensile testing of parts built in different orientations. Mechanical characteristics such as Young's modulus, yield strength (YS), ultimate tensile strength (UTS), and ductility are evaluated. The strain rate effect on mechanical behavior, namely, strength and ductility, is also investigated by testing the material at a range of strain rates from 10−2 to 10−4 s−1. Local mechanical properties were extracted using nanoindentation technique and compared against global values (average values obtained by tensile tests). Although the properties obtained in this experiment were comparable with literature findings, test results showed that in-plane properties, elastic modulus, YS, and UTS are significantly higher than out-of-plane properties. This could be an indication of defects in between layers or imperfect bonding of the layers. Strong positive strain rate sensitivity was observed in out-of-plane direction. The strain rate sensitivity evaluation did not show strain rate dependency for in-plane directions. Local mechanical properties obtained through nanoindentation confirmed the findings of tensile test and also showed variation of properties caused by geometry.