Regression calibration is one of the most commonly used bias-reduction technique in measurement error modelling. However, Tweedie’s formula, originally discovered for normal measurement errors, has never been used for regression calibration, instead, many approximate algorithms are developed for the same purpose. In this talk, we shall introduce a set of Tweedie-type formulae not only for multivariate normal measurement error, but also for multivariate Laplace measurement error, a typical case of the ordinary smooth cases. Potential applications of these Tweedie-type formula in parametric/semiparimatric regression models, neural networks with measurement errors will be also discussed.