This work is concerned with the simulation of magnetovolume effects in the Fe-Ni and FeRh transition-metal alloys as well as in the Laves-phase compound YMn2 and the closely related pseudobinary compounds YxSc1-xMn2 and Y(Mn-Al)2. These materials show a strongly reduced (or vanishing) thermal expansion coefficient (Invar effect) combined with an enhanced compressibility. The opposite effect of a strongly enhanced thermal expansion (anti-Invar effect) can also be observed in these materials. Ab initio calculations suggest, that these anomalies are caused by the magnetic instability of one of the transition metal atoms. In this work this instability is modeled by a generalized Blume-Capel Hamiltonian. The use of a spin-1 Ising model allows for a treatment of the distinct magnetic states of the transition metal atoms within the framework of a localized spin model. The different magnetic states are represented by the spin states 0 and ±1, respectively. Unlike quantum mechanical approaches, this model can be easily evaluated at finite temperatures. The coupling between magnetic and spatial degrees of freedom have been taken into account in two different ways. In the case of Fe-Ni and YMn2 this is achieved by spin dependent pair potentials. In analogy to the 2-γ-states model by Weiss, a change of the spin state is connected with an alteration of the equilibrium lattice constant. In the case of Fe-Rh, the magnetovolume-effects are caused by exchange parameters depending on the inter-atomic distance. The model parameters are determined by comparison with experimental quantities and the results of ab initio calculations. In the case of YxSc1-xMn2 and Y(Mn-Al)2 KKR-CPA calculations were carried out for this purpose. The computation of thermodynamical quantities at finite temperatures was performed using the Monte Carlo method. A separate program was developed for this purpose, which can be used efficiently on massive parallel computers. The calculations show that the most important magnetovolume anomalies of Fe-Ni alloys - and also of the above mentioned Y-Mn compounds - can be reproduced with the Weiss-like model proposed in this work. The change of the behavior, which shows up when physical pressure is applied or the composition is altered, is reproduced qualitatively. This approach was extended to the simulation of Fe-Ni nanoparticles. The transition from bulk to small clusters changes the magnetic and elastic properties of the material in a peculiar manner. The simulations concerning FeRh demonstrate, that a simple statistical model can explain the occurrence of a temperature driven metamagnetic phase transition. The magnetovolume effects and the large change of entropy connected with the phase transition are described by an exchange parameter depending linearly on the interatomic distance.