Abstract: Some strategies for solving the extreme value problems related to multivariate functions were summed up, including the elimination strategy, commutation strategy, principal element strategy, variables introduction strategy, construction strategy, combination strategy of number and form, symmetry strategy, etc., of which the elimination strategies include substitutional elimination, incremental elimination, matching elimination, reduction elimination and so forth;The substitution strategy includes trigonometric substitution, integral substitution and so on.The strategy related to the introduction of variables includes the introduction of one parameter, two parameters as well as multiple parameters.Inequality strategy contains methods like mean inequality, Cauchy inequality, elliptic inequality, power reduction inequality, weighting inequalities, etc.Construction strategy includes constructed function, constructed complex numbers, constructed duality and constructed vectors and so on.The application of the combined strategy of numbers and shapes together with the symmetric strategies in solving the extreme value problems related to multivariate functions is found to be quick and concise.These strategies and methods have been used to analyze and solve some typical problems.