The present work deals with computation of the stress field caused by UV-induced densification in optical fibre cores during Bragg grating elaboration. The stress field is calculated using the finite element method and leads to a contribution to the refractive index modulation being perpendicular to the direction of propagation. The birefringence associated with the stress field is evaluated. Another important result is the growth of a shear stress component developed during Bragg grating writing. This can contribute to the fragilization of fibres. We suggest that these shear stresses are involved in the triggering of a refractive index contribution opposite to the one of the densification which is a negative one associated with the so-called type IIA Bragg grating.