Conventional ultrasonic thickness measurement is to be considered as the assumption that the ultrasonic velocity is known. In actual applications the velocity is often not well known and access is often limited to one side. This paper aims at determining the ultrasonic velocity and thickness of plates with parallel or wedged surfaces using contact measurements made on one surface only. For wedged plates the thickness at one point and the wedge angle are determined. Equations are used for determining the ultrasonic velocity, thickness and wedge angle of the plate based on the times-of-flight measured by two contact transducers coupled to one surface. The time-of-flight of the obliquely reflected longitudinal wave echo was measured as a function of the separation between the two transducers. In addition, a simulation was made for comparing the experimental data and a FEM image. Experiments and simulations were performed on flat and wedged plates of aluminium materials; the calculated results for the unknown quantities are generally agreed with them to some degree.