The interaction of epsilon-near-zero (ENZ) materials with two dimensional parallel-plate waveguide has been analyzed. Electromagnetic wave energy squeezing and supercoupling effects are verified using the full wave simulations. Lower-frequency resonant peak, characteristic peak, higher-frequency resonant peak was observed by varying the shape of the waveguide filled with ENZ materials. It is shown that the position of lower-frequency resonant peak is dependent on ENZ materials, and the position of higher-frequency resonant peak is dependent on Fabry-Pérot resonances. Red shift of the resonant peak is observed by selective tuning the permittivity of the materials in the supercoupling region, and lower-frequency resonant peak is on the left-hand side of characteristic peak. Based on the properties of ENZ materials, two potential applications for optical sensor and optical power divider are suggested and numerically studied. In the wavelength range of 1.2～2 μm, sensitivity of the optical sensor is Δλ/Δε=100 nm; Insertion loss of the optical power divider is 0 dB at 1.3 μm. Simulating results show that ENZ materials with intriguing electromagnetic properties are favorable for the tailoring optical sensor and power divider, and may have interesting potential applications in optical communication and optoelectronics devices.