[Object] To provide a high strength Cr-Ni alloy material excellent in hot workability and stress corrosion cracking resistance, and seamless pipe for oil well. [Solution] A high strength Cr-Ni alloy material which consists of, by mass percent, C: 0.05% or less, Si: 0.05 to 1.0%, Mn: 0.01% or more and less than 3.0%, P: 0.05% or less, S: 0.005% or less, Cu: 0.01 to 4%, Ni: 25% or more and less than 35%, Cr: 20 to 30%, Mo: 0.01% or more and less than 4.0%, N: 0.10 to 0.30%, Al: 0.03 to 0.30%, O (oxygen): 0.01% or less, and REM (rare earth metal): 0.01 to 0.20%, with the balance being Fe and impurities, and also satisfies the conditions in the following formula (1). N × P / REM ‰¤ 0.40 where P, N, and REM in the formula (1) respectively denote the contents (mass%) of P, N, and REM. The high strength Cr-Ni alloy material may further contain one or more types of W, Ti, Nb, Zr, V, Ca, and Mg, instead of part of Fe.