In this work the modulation instability of quasimonochromatic wave packets propagating in conservative media with quadratic nonlinearity and linear nondamped oscillators attached to each point of a continuum is analyzed. Various density distributions of oscillators on natural frequencies are considered and carrier frequency ranges of unstable wave packet propagation are determined. It is shown that instability is closely related to the fact that the resonant dispersion relation can have many branches and thus permit phase-group synchronism between long and short waves. A wave packet propagating under the synchronism condition generates long-wave disturbances (with wavelengths near envelope width) and transmits up to one-half of its initial energy to them. The possible application of this effect for evaluation of microcavities size distribution in imperfect solids is considered.