Mr. Mc Gilvary has been serving a 30-year sentence for unlawful killing.
He is described as having a scorpion tattoo on the right side of his neck, an eagle tattoo on his chest and upper left arm and a tattoo of the words “only god can judge me” on his stomach.
Mr. Mohammed, also known as Redo, is 34 years of age and has been serving a 12 year sentence for robbery with aggravation.
He has a distinguishing bullet wound scar near his Adams apple.
Members of the public are advised that both men are considered to be armed and dangerous and should not be approached if spotted.
The Prison Service explains that if seen, citizens are advised to call the emergency lines E999 or 555 or to contact the nearest police station with relevant information.