The theory of lower hybrid (LH) waves trapped in striations in warm ionospheric plasma in the three-dimensional case is presented. A specific mechanism of trapping associated with the linear transformation of waves is discussed. It is shown analytically that such trapping can take place in elongated plasma depletions with the frequencies below and above the lower hybrid resonance frequency of the ambient plasma. The theory is applied mainly to striations generated artificially in ionospheric modification experiments and partly to natural plasma depletions in the auroral upper ionosphere. Typical amplitudes and transverse scales of the trapped LH waves excited in ionospheric modification experiments are estimated. It is shown that such waves possibly can be detected by backscattering at oblique sounding in very high frequency (VHF) and ultra high frequency (UHF) ranges.