We present the calculations of the gamma-ray flux produced by neutralino annihilation (χ+χ→γ+γ) in our Galaxy. Most attention is paid to the case in which the dark matter in and outside our Galaxy consists of neutralinos. It is shown that in this case the flux is essentially determined by only two physical quantities: the critical density ϱ c =1.1×10 -29g/cm 3 and the local (solar neighbourhood) density of dark matter ϱ ⊙≅0.3 GeV/cm 3. Detectors of large area ( S⩾10 5 cm 2) and very high energy resolution ( ΔE E ∼10 -4−10 -5 ) are needed for the detection of the predicted flux ( I γ ≲1×10 -12cm -12s -1sr -1). A (marginally) detectable gamma-ray flux is found only for an extreme combination of assumptions: the neutralino is almost a pure photino, the lightest sfermion is a slepton with mass ∼50 GeV, and the average density of neutralinos in the Universe is ω χ = 0.03.