A tactile position sensing system based on the sensing of acoustic waves and analyzing with artificial intelligence is proposed. The system comprises a thin steel plate with multiple piezoelectric transducers attached to the underside, to excite and detect Lamb waves (or plate waves). A data acquisition and control system synchronizes the wave excitation and detection and records the transducer signals. When the steel plate is touched by a finger, the waveform signals are perturbed by wave absorption and diffraction effects, and the corresponding changes in the output signal waveforms are sent to a convolutional neural network (CNN) model to predict the x- and y-coordinates of the finger contact position on the sensing surface. The CNN model is trained by using the experimental waveform data collected using an artificial finger carried by a three-axis motorized stage. The trained model is then used in a series of tactile sensing experiments performed using a human finger. The experimental results show that the proposed touch sensing system has an accuracy of more than 95%, a spatial resolution of 1 × 1 cm2, and a response time of 60 ms.