Mn1-xCoxFe2O4 (x=0, 0.25, 0.5, 0.75, and 1) nanoparticles were synthesized using the sol-gel technique. The effect of Co substitution on the structural, elastic, and magnetic properties was systematically studied using X-ray diffraction (XRD) spectroscopy, Fourier transform infrared (FTIR) spectroscopy, and vibrating sample magnetometer (VSM). XRD patterns elucidate the formation of the cubic spinel phase for all prepared samples. Secondary Mn-oxid phases were observed for samples with low Co content x<0.5. All the samples fitted were with Rietveld refinement using Maud software to obtain the lattice parameter (aexp) and particle size (DMaud). Values of the lattice parameter were calculated theoretically and showed a good agreement with aexp. The particle size was calculated from the Williamson and Hall plot and then compared to DMaud, where considerable differences were observed. FTIR measurements confirm the formation of the cubic spinel phase and the elastic moduli were calculated. The magnetic parameters showed a strong dependence on the Co content. The saturation magnetization (Ms) and coercivity (Hc) increased by increasing x. By fitting the magnetic hysteresis loops of different Mn1-xCoxFe2O4 nanoparticles, the effective magnetic anisotropy constant K and the anisotropy field (Ha) were obtained.