In this paper, we present a technique for the deposition of inks, toners, organic polymers, fuels, small solid particles, biological and chemical fluids, using a fluid ejector. The ejector design is based on a flextensional transducer that excites the axisymmetric resonant modes of a clamped circular plate. It is constructed by depositing a thin piezoelectric annular plate onto a thin, edge clamped, circular plate. Liquids or solid-particles are placed behind one face of the plate which has a small orifice at its center. By applying an ac signal across the piezoelectric element, continuous or drop-on-demand ejection of fluids has been achieved. The ejected drop size ranges in diameter from 4 μm at 3.5 MHz to 150 μm at 7 kHz, the corresponding ejected drop volume ranges from 34 fl to 1.5 nl, and the corresponding flow rate ranges from 117 nl/s to 10 μl/s. The unique features of the device are that the fluid is not pressurized, the fluid container is chemically or biologically compatible with most fluids, and the vibrating plate contains the orifice as the ejection source. The device is manufactured by silicon surface micromachining and implemented in the form of two-dimensional arrays. Individual elements are made of thin silicon nitride membranes covered by a coating of piezoelectric zinc oxide. Classical thin plate theory and Mindlin plate theory are applied to derive two-dimensional plate equations for the transducer, and to calculate the coupled electromechanical field variables such as mechanical displacement and electrical input impedance. In these methods, the variations across the thickness direction vanish by using the bending moments per unit length or stress resultants. Thus, two-dimensional plate equations for a step-wise laminated circular plate are obtained as well as two different solutions to the corresponding systems. An equivalent circuit of the transducer is also obtained from these solutions.