Finite Gaussian mixtures are widely used in various fields of science and applications: mathematical modeling, image recognition, spectroscopy, biology, medicine, chemistry, geology, meteorology, marine fisheries and others [2, 6, 7, 11], due to their properties such as identifiability, completeness and resolution [6, 10]. Popularity of finite Gaussian mixtures makes it necessary to solve such mathematical problems as estimation of modes and preliminary evaluation of their number. Well-known papers (see, e.g., [7, 8]) propose algorithms for calculations of the modes, based on well-known computational methods, but are not strictly mathematically justified. In this paper we give a mathematically justified algorithm to calculate all stationary points (SP) of probability density f(x) of finite mixture of normal distributions with equal variances σ and different means μi, i = = 1, 2, . . . , k, 2 k < ∞, taken with their prior probabilities πi ∈ (0, 1) under condition that distribution parameters are known. Stationary points of function f(x) are the roots of equation f ′(x) = 0, which is reduced to two equivalent equations x = φ(x), x = ζ(x). It is proven that all stationary points of continuous monotonically increasing operators φ(x) and ζ(x) = (1 + λ)x − λφ(x) lie on the segment [μ1, μk], μ1 < μ2 < . . . < μk. An algorithm to calculate SP’s is based on Picard’s method of successive approximations (MSA) [4, 5]. Modes and the inflection points of f(x) are found with the use of operator φ, and minimums and inflection points are found with the use of operator ζ.