Hydrogen migration under thermal stress gradient in zirconium alloys results in formation of hydride blisters [1]. An array of blisters makes Zirconium alloy components of nuclear reactors susceptible to fracture [2]. The whole process of hydride blister formation and fracture of these components is very complex and involves hydrogen migration under thermal gradient, hydride precipitation, straining of the matrix, setting up of hydrostatic stress gradient, enhanced hydrogen migration under the combined influence of thermal and stress gradient, stress-reorientation of hydrides [3], cracking of hydrides, crack growth by delayed hydride cracking mechanism [4], interlinking of blisters and spontaneous fracture of the component. In this work we estimate the stress components in hydride blisters and the surrounding matrix for certain assumed blister depths. The estimated stress predicts the hydride orientation in the matrix surrounding the blisters and will be subsequently used to model the hydrogen diffusion under hydrostatic stress and temperature gradients.