The knowledge of needle location during insertions is essential for the success of interventional radiology procedures. As the needle is susceptible to undergo deformations during its insertion into tissues, several methods have been proposed to monitor the needle deformed shape. Thus, instrumented needles with U-shaped strain gauges are currently being developed to reconstruct the shape of the needle from gauge acquisitions. These acquisitions are used in combination with gauge model to obtain estimate of the strain of the needle. The current modeling is limited as it does not consider the geometry of the gauge. This paper introduces a more complete model for U-shaped strain gauge which, on the difference of the current model, takes into account the width of the gauge. Thus, the impact of width modeling on the strain estimate can be measured and used to improve strain estimation accuracy. Results with real characteristics of instrumented needle devices show that the differences of strain estimate are around few percents. Finally, by taking into account the width and the length of the gauge our model includes the effets of the gauge size on the strain estimation and makes the miniaturization of the gauge less necessary.