The simple but realistic model described by a Heisenberg Hamiltonian with nearest neighbOurs and next nearest neighbours interactions in an external magnetic field was investigated by use of the Monte Carlo method, Three-dimensional vector spins of length ~ were distributed randomly on a fcc lattice. Different concentrations of spins, x ffi 0.05, 0.10 ..... 0.90, were studied. For low concentrations, simulated samples contained about 1000 spins. For higher values ofx the size of system was about 8000. All the computations were done for high external magnetic fields of around 3 T. During simulation, physical quantities such as magnetization, energy, specific heat and magnetic susceptibility were determined. The results for magnetization differ for the zero-field-cooled (ZFC) and field-cooled (FC) cases for the whole range of concentrations. This difference, also typical for experimental data, seems to vanish after longer simulation. From critical temperatures for'~ computer simulated magnetization, the magnetic phase diagram was obtained and compared to experimental data foi" Cdl_=MnxTe. Concentration dependent results for magnetization, specific heat and magnetic susceptibility allowed on6 to distinguish three different regions for the simulated system: x < 0.20, 0.30 < x < 0.60, 0.70 < x < 0.90. Cdl_xMnxTe, a member of this group of materials, crystalli7~es in zinc-blende structure over the whole x <0.70 range [2]. The Cd 2+ and Mn 2+ ions randomly populate a fcc sublattice. Manganese ions are mainly coupled by the nearest neighbour (NN) antiferromagnetic (AF) superexchange interaction. The next nearest neighbour (NNN) and more distant interactions are weaker and decrease very rapidly with distance between the Mn ions [3]. The value of J~NW is not well known and is believed to be in range 0.1-0.25 of the NN exchange constant [4][5][6].The fcc lattice with AF couplings does not allow to simultaneous minimization of energies of all exchange bonds and thus leads to frustration. Randomness and frustration are two essential factors thought to be respgnsible for the spin-glass behaviour observed experimentally in SMSC [7].In our paper we present a simple computer model of such materials ~nd compare Monte Carlo simulation results wi~ available experimental data. Such an approach was used by Kett, Gebhardt and Krey [8] to investigate magnetization behaviour of Cd0.4iMn0.55Te mixed crystals in high external magnetic fields. We extended use of this model for the whole range of concentrations of Mn ions (including the physically inaccessible values of x -0.80, 0.90) and determined also i the energy, magnetic s~sceptibility and specific heat.In section 2 the details of the model, definitions of observed physical quantities~ and procedures of 0304-8853/90/$03.50 © 1990 -Elsevier Science Publishers B.V. (North-Holland)