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We study the eigenmodes of optical Tamm states (OTSs) at metal-distributed Bragg reflector interface. A peculiar type of non-propagating OTSs, named as evanescent OTSs, is found with mode propagation constant exhibiting the imaginary part to be much larger than the real part. The existence of such evanescent OTSs is attributed to the extension of Bragg forbidden band under complex propagation constants. An analytical solution of the evanescent OTSs is derived. Compared with propagating OTSs, transverse magnetic-polarized evanescent OTSs are found to exhibit more strongly localized field distributions associated with enhanced surface field intensity, which may be beneficial for surface-related applications such as sensing. Potential application as modulators is also demonstrated by using the nearly vertical dispersion characteristics around the transition wavelength between propagating OTSs and evanescent OTSs.