Chemical kinetic studies of hydrogen atom abstraction reactions by hydroperoxyl (HȮ2) radical from six alkyl cyclohexanes of methyl cyclohexane (MCH), ethyl cyclohexane (ECH), n-propyl cyclohexane (nPCH), iso-propyl cyclohexane (iPCH), sec-butyl cyclohexane (sBCH), and iso-butyl cyclohexane (iBCH) are carried out systematically through high-level ab initio calculations. Geometry optimizations and frequency calculations for all species involved in the reactions are performed at the M06-2X/6-311++G(d,p) level of theory. Electronic single-point energy calculations are calculated at the UCCSD(T)-F12a/cc-pVDZ-F12 level of theory, with zero-point energy corrections. High-pressure limit rate constants for the reactions of alkyl cyclohexanes + HȮ2, in the temperature range of 500-2000 K, are calculated using conventional transition state theory taking asymmetric Eckart tunneling corrections and the one-dimensional hindered rotor approximation into consideration. Elementary reaction rate constants and branching ratios for each alkyl cyclohexane species were investigated, and rate constant rules of primary, secondary, and tertiary sites on the side-chain and the ring are provided here. Additionally, temperature-dependent thermochemical properties for reactants and products were also obtained in this work. The updated kinetics and thermochemistry data are used in the alkyl cyclohexane mechanisms to investigate their effects on ignition delay time predictions of shock tube and rapid compression machine data, and species concentrations from a jet-stirred reactor. It is found that these investigated reactions promote ignition delay times in the temperature range of 800-1200 K and also improve the prediction of cyclic olefin species formation which stems from the decomposition of fuel radicals.