The structures and properties of materials are profoundly altered under high pressure due to a large change of atom spacing, chemical bonding and Gibbs free energies. Therefore, materials with novel structures and properties can be created via a process known as pressure-induced phase transition. Here we report the investigations of pressure effects on the elastic properties and the glass transition of Zr-, Pd-based bulk metallic glasses (BMGs). The elastic constants and the Debye temperatures, of a Zr₄₁Ti₁₄Cu_12.5Ni₁₀Be_22.5C₁ and a Pd₃₉Ni₁₀Cu₃₀P₂₁ BMGs are measured by using an ultrasonic technique, and their pressure dependence is exhibited. The equations of state (EOS) of the two BMGs are established. The acoustic attenuation behaviors are also monitored with various pressure in the two BMGs, and a marked difference between the two BMGs is revealed. The effects of pressure-induced structural relaxation on the glass transition of the Pd₃₉Ni₁₀Cu₃₀P₂₁ BMG are investigated by a temperature-modulated differential scanning calorimetry technique. The pressure dependence of the reversible and irreversible glass transition is explained.