A numerical approach is proposed to assess the high cycle fatigue (HCF) strength of periodic cellular structures produced by Selective Laser Melting under multiaxial loads. The model is based on a general numerical homogenisation scheme and an explicit description of the Elementary Cell (EC) combined to an extreme values analysis making use of a fatigue indicator parameter based on Crossland’s criterion. This method is applied to 33 EC topologies.In addition, geometric discrepancy and surface roughness are experimentally characterised and considered in the numerical model using three methods which are compared to the experimental HCF strength.