Modelling of tissue mimicking phantoms play a crucial role in the development of Ultrasound Elastography. This paper deals with both computer modelling and physical design of agar based tissue mimicking phantoms with embedded inclusions of varying stiffness in uniform homogeneous background. The elastic properties of agar based phantom are imaged using Ultrasound Elastography. The computer modelling and linear strain analysis of the phantom are done using finite element method. The visual display of strain results are compared with the experimental results and they are in good agreement. This allows us to model many hypothetical structures of real life and will be useful while validating signal processing algorithms for new imaging modalities. © 2012 IEEE.