The present paper is primarily focused to understand the strain driven alterations in thermoelectric properties of two-dimensional SiH and GeH monolayers from first-principle calculations. Electronic band structures and the associated thermoelectric properties of the compounds under ambient and external strains have been critically unveiled in terms of Seebeck coefficients, electrical conductivities, power factors and electronic thermal conductivities. The phonon dispersion relations have also been investigated to estimate the lattice thermal conductivities of the systems. The thermoelectric figure of merits of SiH and GeH monolayers under ambient and external strains have been explored from the collective effects of their Seebeck coefficients, electrical conductivities, electronic and lattice thermal conductivities. The present study will be helpful in exploring the strain induced thermoelectric responses of SiH and GeH compounds which in turn may bear potential applications in clean and global energy conservation.