Additive manufacturing (AM) enables fine control over the architecture and mechanical properties of porous lattice structures. Typical periodic unit cells used in porous structures are inherently anisotropic, may not be suitable for multi-axial applications and cannot reliably create features or struts with low build angle. This study used laser powder bed fusion (PBF) to create isotropic stochastic porous structures in stainless steel (SS316L) and titanium alloy (Ti6Al4V), with modifications that aimed to overcome PBF manufacturing limitations of build angles. The structures were tested in uniaxial compression (n = 5) in 10 load orientations relative to the structure, including the three orthogonal axes. The testing verified that no hidden peaks in elastic modulus existed in the stochastic structure. Modification to the structure reduced the standard deviation of the 10 elastic modulus values from 249 MPa to 101 MPa when made in SS316L and from 95.9 MPa to 52.5 MPa for Ti6Al4V, indicating the structures were more isotropic. These modified stochastic structures have improved stiffness isotropy and could be used for lightweighting and biomaterial applications, reducing the dependence of performance on build orientation, and allowing more flexibility for component orientation on the build platform.