We consider the trapping of low refractive index objects, such as ultrasound contrast agent microbubbles, in a dual-beam fibre-optic trap. We confirm numerically that such a configuration results in stable trapping and we present the calculated trapping forces and spring constants. Furthermore we calculate the photonic stress profile over the surface of the trapped microbubble using both ray optics and Mie scattering approaches, and compare the results. We then find the optical stress-induced deformation of the microbubble for both the ray optics and Mie scattering stress profiles using linear elastic membrane theory. We suggest that this method could be a useful tool for quantifying the mechanical properties of the shell material of an ultrasound contrast agent microbubble.