The study of vegetable tissue is essential in plant growth analysis. The elasticity is an important characteristic when firmness is studied in fruits or when turgidity is tested in plant leaves. This property gives information about the ripeness of fruits, the water content in leaves, and, in general, the morphological and physiological state of plants. Hence, the propagation of elastic waves in these media is a useful tool that gives information about the developmental stage of the plant. In this sense, laser ultrasonics is a promising method in the characterization of composite materials. In a certain way, vegetable tissues can be thought of as a kind of biological composite abstracted as a stratified plate of several layers. In this work, as a first approximation, we propose a methodology to generate guided waves in vegetable tissues by using laser ultrasonics techniques. We implement a pulsed laser system to induce ultrasonic waves without damage on the samples. Besides, we develop a methodology for processing the propagated acoustic waves. This analysis allows us the assessment of dispersive properties, a useful tool when determining important descriptors such as firmness index, water content, and provide useful information to feed biophysical models, among others.