We consider a solution of the atmospheric neutrino problem based on oscillations of muon neutrinos to sterile neutrinos: $ u_{mu}$ $leftrightarrow$ $ u_s$. The zenith angle ($Theta$) dependences of the neutrino and upward-going muon fluxes in presence of these oscillations are studied. The dependences have characteristic form with two dips: at $cos Theta = -0.6 div -0.2$ and $cos Theta = -1.0 div -0.8$. The latter dip is due to parametric resonance in oscillations of neutrinos which cross the core of the earth. A comparison of predictions with data from the MACRO, Baksan and Super-Kamiokande experiments is given.
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