Herein, we demonstrate that first-principles calculations can be used for mapping of the electronic properties of two-dimensional (2d) materials with respect to nonuniform strain. By investigating four representative single-layer 2d compounds with different symmetries and bonding characters, namely, 2d-MoS2, phosphorene, α-Te, and β-Te, we reveal that such a mapping can be an effective guidance for advanced strain engineering and the development of strain-tunable nanoelectronics devices, including transistors, sensors, and photodetectors. Thus, we show that α-Te and β-Te are considerably more elastic compared to the 2d compounds with strong chemical bonding. In the case of β-Te, mapping uncovers the existence of curious regimes where nonuniform deformations allow one to achieve unique localization of band edges in momentum space that cannot be realized under either uniform or uniaxial deformations. For all other systems, the strain mapping is shown to provide deeper insight into the known trends of band-gap modulation and direct-indirect transitions under strain. Hence, we prove that the standard way of analyzing selected strain directions is insufficient for some 2d systems, and a more general mapping strategy should be employed instead.