In this paper, explicit models of time and frequency dependent effective properties of transversely isotropic viscoelectroelastic composites are elaborated. Based on the principle of linear viscoelectroelasticity and the Mori-Tanaka micromechanical mean field approach, the effective properties are derived in the Laplace-Carson domain and then inverted analytically or numerically to the time domain . Using compact matrix formulation, explicit relationships are obtained for different effective viscoelectroelastic moduli of piezoelectric materials with various inclusions shapes. Results based on the elaborated effective viscoelectroelastic models are presented for various types of piezoelectric inclusions and compared to the available predictions. These models are suitable for designers to predict viscoelectroelastic moduli of composite materials with optimized characteristics.