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Abstract Motivated by properties-controlling potential of the strain, we investigate strain dependence of structure, electronic, and magnetic properties of Sr 2 IrO 4 using complementary theoretical tools: ab-initio calculations, analytical approaches (rigid octahedra picture, Slater-Koster integrals), and extended $$t-{{{\mathcal{J}}}}$$ t − J model. We find that strain affects both Ir-Ir distance and Ir-O-Ir angle, and the rigid octahedra picture is not relevant. Second, we find fundamentally different behavior for compressive and tensile strain. One remarkable feature is the formation of two subsets of bond- and orbital-dependent carriers, a compass-like model, under compression. This originates from the strain-induced renormalization of the Ir-O-Ir superexchange and O on-site energy. We also show that under compressive (tensile) strain, Fermi surface becomes highly dispersive (relatively flat). Already at a tensile strain of 1.5%, we observe spectral weight redistribution, with the low-energy band acquiring almost purely singlet character. These results can be directly compared with future experiments.