Two different groups of solid polymer sheets: low density polyethylene (LDPE) sample of thickness 0.006 cm and 0.007 cm along with high density polyethylene (HDPE) sample of the thickness of 0.009 cm, 0.010 cm were taken in this work. The measurement of electrical properties such as dielectric constant, ε' and dielectric loss, ε'' for LDPE and HDPE polymer sheets have been measured using a dielectric cell. The dielectric cell has been fabricated which consists of two circular parallel plates of pure stainless steel each of 5 cm diameter and 2 mm thickness. An impedance bridge (GRA 650A) was used for measurement of capacitance, C, and dissipation factor, D in the audio frequency (AF) range, 100 Hz to 10 kHz. Different samples were loaded in between the two plates of the cell and the capacitance as well as the dissipation factor were estimated from the dial readings of the bridge. Effect of frequency variation on ε', ε'', relaxation time, τ , dissipation factor, tanδ and ac conductivity, σ were also discussed at audio frequency range. The complex permittivity, ε*, related to free dipole oscillating in an alternating field and loss tangent, tanδ were calculated. The frequency-dependent conductivity, dielectric behavior, and electrical modulus, both real (M') and imaginary (M") parts of LDPE and HDPE have been studied in this work. The values of the real part of the electrical modulus (M') did not equal to zero at low frequencies and it is expected that the electrode polarization may develop in both sheets. These findings reveal an increased coupling among the local dipolar motions in a short-range order localized motion. The analysis of real (ε') and imaginary (ε'') parts of dielectric permittivity and that electrical modulus real (M') and imaginary (M") parts signify poly dispersive nature of relaxation time as observed in Cole-Cole plots.