This paper investigates the use of the body terminal of MOS transistors to improve the linearity of some key circuits used to implement analog and mixed-signal circuits integrated in Fully Depleted Silicon on Insulator (FD-SOI) CMOS. This technology allows to increase the body factor with respect to conventional (bulk) CMOS processes. This effect is analyzed in basic analog building blocks -such as switches, simplestage transconductors and Voltage-Controlled Ring Oscillators (VCROs). Approximated expressions are derived for the nonlinear characteristics and harmonic distortion of some of these circuits. As an application, transistor-level simulations of two VCRO-based Σ∆ modulators designed in a 28-nm FD-SOI CMOS technology are shown in order to demonstrate the benefits of the presented techniques.