Abstract: Simultaneous trapping of multiple ultra-cold atomic species presents a starting point for a wide range of experiments such probing strongly interacting quantum gases, exploring aspects of superfluidity, and study induced interspecies scattering resonances. It is also an important step toward synthesis of stable, polar molecules, which may be used to study new dipolar quantum superfluids, as building blocks in scalable quantum computing schemes, and as sensitive probes of fundamental physics. We choose lithium (Li) and ytterbium (Yb) atoms as the two constituent species of our experiment for several reasons. Both Li and Yb possess stable bosonic and fermionic isotopes which have been brought to quantum degeneracy in single species experiments. Li is a one-electron atom and Yb is a two-electron atom, allowing for species selective trapping techniques using external magnetic fields, as well as magnetic trapping of synthesized, diatomic LiYb molecules. A large electric dipole moment in the molecular ground state allows for studies of strongly dipolar quantum gases, and makes LiYb a promising candidate for a sensitive electron EDM measurement. We achieve simultaneous magneto-optical traps (MOTs) of lithium and ytterbium. Because the two MOTs are optimized at different magnetic field settings, the species are loaded in optical dipole trap sequentially; Yb is allowed to fully load, and is then transferred to a far off-resonant optical dipole trap, (ODT) before Li is introduced into the system. After transferring the Li to the ODT we routinely obtain ~1 million optically trapped atoms of each species, at temperatures of about 100 μK. We use obtained Li-Yb mixture in ODT for study of its collisional stability, furthermore we observe thermalization of the mixture that allows us to extract collisional cross-section of ultra-cold Li and Yb atoms.