Cyanobacteria are prokaryotic organisms that capture energy from sunlight using oxygenic photosynthesis and transform CO2 into products of interest such as fatty acids. Synechococcus elongatus PCC 7942 is a model cyanobacterium efficiently engineered to accumulate high levels of omega-3 fatty acids. However, its exploitation as a microbial cell factory requires a better knowledge of its metabolism, which can be approached by using systems biology tools. To fulfill this objective, we worked out an updated, more comprehensive, and functional genome-scale model of this freshwater cyanobacterium, which was termed iMS837. The model includes 837 genes, 887 reactions, and 801 metabolites. When compared with previous models of S. elongatus PCC 7942, iMS837 is more complete in key physiological and biotechnologically relevant metabolic hubs, such as fatty acid biosynthesis, oxidative phosphorylation, photosynthesis, and transport, among others. iMS837 shows high accuracy when predicting growth performance and gene essentiality. The validated model was further used as a test-bed for the assessment of suitable metabolic engineering strategies, yielding superior production of non-native omega-3 fatty acids such as α-linolenic acid (ALA). As previously reported, the computational analysis demonstrated that fabF overexpression is a feasible metabolic target to increase ALA production, whereas deletion and overexpression of fabH cannot be used for this purpose. Flux scanning based on enforced objective flux, a strain-design algorithm, allowed us to identify not only previously known gene overexpression targets that improve fatty acid synthesis, such as Acetyl-CoA carboxylase and β-ketoacyl-ACP synthase I, but also novel potential targets that might lead to higher ALA yields. Systematic sampling of the metabolic space contained in iMS837 identified a set of ten additional knockout metabolic targets that resulted in higher ALA productions. In silico simulations under photomixotrophic conditions with acetate or glucose as a carbon source boosted ALA production levels, indicating that photomixotrophic nutritional regimens could be potentially exploited in vivo to improve fatty acid production in cyanobacteria. Overall, we show that iMS837 is a powerful computational platform that proposes new metabolic engineering strategies to produce biotechnologically relevant compounds, using S. elongatus PCC 7942 as non-conventional microbial cell factory.