The stability of pressure driven modes such as the 1/1 internal kink is known to depend sensitively on a multitude of physical effects such as toroidal rotation, kinetic effects due to thermal and suprathermal particle species and finite Larmor radius effects. Presently available models do not take into account these combined effects in a consistent way. This thesis presents the derivation of a novel kinetic-MHD model utilizing a kinetic pressure closure which incorporates all of these physical mechanisms and can in particular be used to study the interplay of important centrifugal and kinetic effects in strongly rotating plasmas. The kinetic-MHD model is based on an original derivation of a consistent set of guiding-centre equations allowing for sonic flow. Important higher-order Larmor radius corrections to the guiding-centre coordinates, which are conventionally discarded, are discussed in detail for two applications: The first application concerns neutral beam injection (NBI) heating. It is shown that higher-order (Ba\~nos drift) corrections affect the expected resonances of particles with resonant magnetic perturbations (RMP), as well as the estimated NBI driven current in slowing-down simulations in a MAST-like equilibrium by up to 8\%. As a second application, the full expression for the gyroviscous contribution to the pressure tensor is obtained from guiding-centre theory. Higher-order guiding-centre corrections are shown to lead to a non-circular Larmor motion of the particle around its guiding-centre which result in off-diagonal components of the pressure tensor. The derived expression for the pressure tensor in terms of the guiding-centre distribution function is used to formulate a consistent linear kinetic-MHD model with kinetic closure for the pressure. The proposed kinetic-MHD model allows for strong flows and includes centrifugal as well as diamagnetic flows. The model also includes a drift-kinetic form of the quasi-neutrality equation, and allows the effects of a parallel electric field on global MHD modes to be studied self-consistently. Pressure closure of the kinetic-MHD model is obtained from a solution of the guiding-centre equations, thus taking into account finite orbit-width effects and particle-wave interactions such as precession resonance. The benefits of the pressure closure approach over an approach following current-closure are discussed. It is shown that due to several convenient cancellations, the pressure closure approach can be based on first-order guiding-centre equations while an equivalent model formulated in terms of current closure would require second-order corrections to be retained. Thus, the benefits and the efficiency of a formulation of kinetic-MHD models with pressure closure over alternative models based on current closure are demonstrated.