To investigate the constitutive relation of a plant tissue regarded as a deformable continuum, stress and strain must be determined experimentally for the same configurations. Such experiments are hindered by the inherent theoretical complexity of continuum mechanics, and by the technical difficulties of effecting external stress loads or body forces on the tissue without invasion, especially on a small scale. An understanding of appropriate mechanical problems and their solutions can help the experimentalist overcome these difficulties to a certain extent. Based on recent work on fiber-reinforced material, we formulate a constitutive theory for the root of different angiosperm species and suggest a set of loading conditions to determine the parameter values in a specific tissue sample. The loading conditions are formulated with a view toward experimental realization in vivo or with minimal invasion. For each loading condition, we formulate the corresponding mechanical problem and show how to obtain the values of the elastic parameters from known solutions. This framework can be used to analyze the interplay between mechanical and metabolic behavior in plants and to study the elastodynamics of plant tissues.