Tables of Lommel''s Functions of Two Pure Imaginary Variables provide tables on cylinder functions of two pure imaginary variables. These tables are computed on the "Strela" electronic computer and are checked and prepared in the Analytic Machine Department. The introductory part describes some properties of the Lommel''s functions. This part also contains the integral forms and asymptotic expansions. Lommel''s functions of two pure imaginary arguments are defined by the Neumann series. This text is of value to researchers and students.