The $K^{\pm }-p$ elastic scattering was measured in a small angular region near 180° ($-0.995\mathrm{}\ge cos{\theta }^{*}\ge -1.0\mathrm{}$) at six momenta from 0.41 to 0.72 $\frac{\mathrm{GeV}}{c}$. The forward-scattered protons were detected with scintillation counters and identified by time-of-flight measurements. The $K^{+}-p$ elastic differential cross section at 180° is found to be essentially constant with a value near 0.9 mb/sr. The sum of the $P$-wave phase shifts ($2{\delta }_{\frac{3}{2}}+{\delta }_{\frac{1}{2}}$) is found to be negative in this momentum region. The $K^{-}$ elastic differential cross section is found to dip to a minimum (0±0.2 mb/sr) at 0.66 $\frac{\mathrm{GeV}}{c}$.

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