Several medical procedures involve the use of needles. The advent of robotic and robot assisted procedures requires dynamic estimation of the needle tip location during insertion for use in both assistive systems as well as for automatic control. Most prior studies have focused on the maneuvering of solid flexible needles using external force measurements at the base of the needle holder. However, hollow needles are used in several procedures and measurements of forces in proximity of such needles can eliminate the need for estimating frictional forces that have high variations. These measurements are also significant for endoscopic procedures in which measurement of forces at the needle holder base is difficult. Fiber Bragg grating sensors, due to their small size, inert nature, and multiplexing capability, provide a good option for this purpose. Force measurements have been undertaken during needle insertion into tissue mimicking phantoms made of polydimethylsiloxane as well as chicken tissue using an 18-G needle instrumented with FBG sensors. The results obtained show that it is possible to estimate the different stages of needle penetration including partial rupture, which is significant for procedures in which precise estimation of needle tip position inside the organ or tissue is required.