This paper investigates the cyclic elastoplastic anisotropy of Ti-6Al-4V manufactured via selective laser melting, caused by different build orientations. Tensile monotonic and cyclic stepped symmetric strain-controlled tests on coupons manufactured at 0 degrees, 45 degrees, and 90 degrees build orientations were performed for both the SLM material and for a mill annealed material. The microstructure characteristics of the SLM material were examined through optical and electron microscopy revealing a unique alpha' martensite microstructure. The examination of the evolving tensile and compressive maximum stresses identified an interesting phenomenon, that of asymmetric cyclic softening. This phenomenon was observed only in the SLM Ti-6Al-4V, while its wrought counterpart confirmed the findings of past research reported in the literature. The residual stresses presented in the SLM coupons had a significant influence on the cyclic behaviour of the material. Mechanical anisotropy in both monotonic and cyclic tests was noticed with the diagonal (45 degrees) coupon having the largest yield stress in both loading conditions. The findings of this research study can be very useful in engineering applications utilising as-built SLM materials.