Thin films are developed by dispersing carbon black nanoparticles and carbon nanotubes (CNTs) in an epoxy polymer. The films show a large variation in electrical resistance when subjected to quasi-static and dynamic mechanical loading. This phenomenon is attributed to the change in the band-gap of the CNTs due to the applied strain, and also to the change in the volume fraction of the constituent phases in the percolation network. Under quasi-static loading, the films show a nonlinear response. This nonlinearity in the response of the films is primarily attributed to the pre-yield softening of the epoxy polymer. The electrical resistance of the films is found to be strongly dependent on the magnitude and frequency of the applied dynamic strain, induced by a piezoelectric substrate. Interestingly, the resistance variation is found to be a linear function of frequency and dynamic strain. Samples with a small concentration of just 0.57% of CNT show a sensitivity as high as 2.5% MPa⁻¹ for static mechanical loading. A mathematical model based on Bruggeman's effective medium theory is developed to better understand the experimental results. Dynamic mechanical loading experiments reveal a sensitivity as high as 0.007% Hz⁻¹ at a constant small-amplitude vibration and up to 0.13%/μ-strain at 0–500 Hz vibration. Potential applications of such thin films include highly sensitive strain sensors, accelerometers, artificial neural networks, artificial skin and polymer electronics.