Fiber reinforced plastics (FRP) is increasingly being used in infrastructural applications like bridges, chemical plants etc., where the environment can limit the expected service life of structures made of conventional materials such as reinforced concrete, steel or timber. Advantages of FRP over conventional constructional materials are its high specific strength and specific stiffness, ease with which it can be moulded to various shapes, corrosion resistance, lower lifecycle cost, durability etc. Estimation of accurate dynamic responses of FRP structures is very important from their operation point of view. Such dynamic responses are functions of material properties, boundary conditions, geometry and applied loading. FRP being an anisotropic and layered composite material, a large number of elastic material property parameters are to be determined. Moreover, its structural fabrication and material fabrication at constituent level being one unified process, the actual existing material property parameters may vary considerably from those specified in established standards or determined from characterisation tests. The present approach attempts at establishing a non-destructive technique based on experimental modal testing and finite element model updating to estimate the elastic material parameters of an 'I' beam made of FRP, thereby making the prediction of dynamic responses more accurate. Static load test on the beam and characterisation tests on samples cut from actual structure are conducted to assess the performance of this updating exercise. The current approach can also be used to non-destructively monitor degradations of elastic material properties over time and thus can be used for health monitoring of existing FRP structures.