We have used a Monte Carlo technique to study two Ising magnetic systems which exhibit tricritical points. The critical behavior of a spin‐1, Blume‐Emery‐Griffiths model on a square lattice was studied over a wide range of zero field splitting parameters Δ. As expected, the critical exponents β, γ, δ, all retained their Δ = 0 values until quite near the tricritical point where all three exponents changed dramatically to take on new “Tricritical values”. In addition, the critical field curve for a spin‐½ metamagnet on a simple cubic lattice was calculated. A tricritical point was observed at T t = 0.58 T N with the critical field being smooth and continuous at the tricritical point. The behavior of the magnetization and susceptibility was contrasted with that found previously for a simple cubic antiferromagnet, but good agreement was found with recent series expansion results on the identical metamagnet.