The Standard Model has been extremely successful at describing nature so far; however, the Standard Model has many deficiencies. It doesn ?t predict many of the phenomena we observe today, such as gravity, dark matter, dark energy, absence of CP violation in strong interactions, etc. Additionally, the Standard Model doesn ?t explain why gravity is so much weaker than the other forces, which is known as the hierarchy problem. These deficiencies have motivated the search for Physics Beyond the Standard Model. Using the Higgs boson, it is possible to probe for signatures of theories Beyond the Standard Model. At the LHC, potential signatures of Higgs interacting with new physics involves the production of Higgs and some other Standard Model particles, which we can observe through standard Higgs discovery channels. We enumerate a number of simplified models involving these exotic Higgs + X productions ( ?X ? stands for the other Standard Model particles produced), and implement these models on software level. These simplified models are governed by basic QFT and Lorentz and gauge invariance. Then we simulate events involving Higgs + X according to these models, run them through hadronization and detector simulations, and implement the same analysis cuts as current experimental searches to calculate the efficiencies for the detection of these new physics signals. Our ultimate goal is to repeat this process for a comprehensive list of simplified models, to see if current experimental analyses cover all the possible Higgs + X signatures, to propose new analyses if there exists any gaps, and to use the calculated efficiencies to constrain these new models.