Open and closed porous structures with lattice and honeycomb geometry can be built using laser powder bed fusion additive manufacturing processes. The porous structures can be used to tailor the mechanical properties of a component or provide other functionality, such as for bone ingrowth in medical implants. Porous structures were created and analysed in this paper both physically and using finite element modelling. It was found that the accuracy of the built parts was reasonable and within the manufacturing processes general tolerance of +/- 50 μm. However, it was noticeable that the corners of the square shape pores were naturally filleted by the manufacturing process. The finite element model was developed using ANSYS software, stress concentrations were observed in the porous structures under loading. In addition to this, fragments of the material were present on the internal surfaces of the pores, which were formed from partially melted powder particles.