A computational method is presented to design alloys of lower susceptibility to solidification cracking, while preventing the formation of porosity and defects during laser powder bed fusion (LPBF). The method is developed for austenitic stainless steels, on which a wealth of data are available as various conditions for crack and pore/defect formation have been reported. The model is based on an alloy design approach combining thermodynamic calculations with a genetic algorithm to discover novel austenitic stainless steel compositions; the new alloys are expected to be crack-free whilst showing improved strength. A new crack prevention factor is proposed to relate composition to solidification crack formation. The factor incorporates quantitative criteria for the solidification temperature range, the performance index (ratio between yield stress and coefficient of thermal expansion) and the solidification path. Overall, the design methodology is validated by literature data on 316L austenitic stainless steel. Although cracking is not an issue during LPBF of 316L stainless steel, this material is a good choice to show under which conditions the cracks form. As for porosity and defect prevention, it is shown how this can be achieved by providing a sufficient amount of energy to melt the powder bed, and by controlling the melt pool geometry; such criteria are dissimilar to those reported in the literature. Process maps have been developed to show the effects of process parameters on the formation of pores and defects based on the proposed criteria. The model is applied to optimise such parameters to produce 316L austenitic stainless steel, and it is shown that a defect-free LPBFed stainless steel can be achieved, performing better under tensile testing compared to its wrought counterpart. The conditions for the application of such model to other alloy families displaying cracking, such as marageing steels and nickel alloys, are discussed.