Butadiene Rubber (BR) was compounded with different compositions of Cloisite 15 and epoxy‐polyester hybrid (EPH), a powder coating waste, using a laboratory‐scale internal mixer at 100°C. Micromechanics of BR/Cloisite 15A (100/3, 100/5, and 100/7), BR/EPH (100/10, 100/20, 100/30, and 100/40) and BR/EPH/Cloisite 15A (100/20/3, 100/20/5, and 100/20/7) compounds were compared to the pure BR through uniaxial tensile and compression measurements. Micromechanical models including Halpin‐Tsai, Leidner‐Woodhams, Pukanszky, and Guth were used to estimate the nanoclay aspect ratio among which Halpin‐Tsai could present more acceptable conclusions confirmed with transmission electron microscopy (TEM). Finite element modeling through constitutive hyper‐elastic models, that is, Arruda‐Boyce, Marlow, Third‐order Ogden, Mooney‐Rivlin, second‐order polynomial, Van der Waals, Neo‐Hooke, and Yeoh was conducted (ABAQUS® software). Simulation results compared with the experimental data suggested that Marlow, Van der Waals, and Yeoh could describe the behavior of this material at whole strain ranges with an acceptable accuracy. POLYM. COMPOS., 39:E2028–E2035, 2018. © 2017 Society of Plastics Engineers