This work presents a systematic analysis on the transient responses of a piezoelectric half space to mixed anti-plane mechanical/in-plane electrical line sources, which is in fact the Lamb's problem for a transversely isotropic piezoelectric half space.¶A key assumption of the classical piezoelectricity theory is the so-called “quasi-static” approximation, and it reduces the Maxwell equations to the charge equation of the electrostatics — an elliptic partial differential equation. Consequently, the dynamic piezoelectricity equations are no longer a hyperbolic system, which then poses serious difficulties in studying the transient behaviors of piezoelectric materials, a problem that has profound engineering significance.¶To circumvent this difficulty, a so-called “quasi-hyperbolic” approximation is introduced in this paper. Under this assumption, the simplified Maxwell-Christoffel equations remain as a hyperbolic system of partial differential equations. Based on the proposed equations, two types of mixed boundary value problems have been solved: (1) anti-plane mechanical line source with boundary surface covered by a conductive film; (2) anti-plane mechanical / in-plane electric line sources with boundary surface abutted to another vacuum half space. In addition to the responses of shear-horizontal (SH) acoustic wave and transverse electric (TE) wave, the closed form solutions obtained here reveal that there exit other transient responses due to the electroacoustic surface wave — the celebrated Bleustein-Gulyaev wave, electroacoustic head wave, as well as a purely electric head wave.