The tetragonal (s.g. I4/nmm; #129) silicide arsenide ZrCuSiAs is well known as a structural type of the broad family of so-called 1111-like quaternary phases which includes now more than 150 representatives. These materials demonstrate a rich variety of outstanding physical properties (from p-type transparent semiconductors to high-temperature Fe-based superconductors) and attracted a great interest as promising candidates for a broad range of applications. At the same time, the data about the electronic and elastic properties of the ZrCuSiAs phase itself, as well as of related silicide arsenides and germanide arsenides are still very limited. Here for a series of six isostructural and isoelectronic 1111-like phases which includes both synthesized (ZrCuSiAs, HfCuSiAs, ZrCuGeAs, and HfCuGeAs) and hypothetical (TiCuSiAs and TiCuGeAs) materials, systematical studies of their structural, elastic, electronic properties and stability trends are performed by means of first-principles calculations.