In the Book of the Prophet Joel, we read: “The beasts of the field cry also unto Thee…” (1:20). Therefore, if God accepts their prayers, then He cares of them. By the way, this last thought can be confirmed by many quotes from the Holy Scriptures, testifying to the providence of God for all the creatures He created, and not just for man who, unlike other creatures, is an image and likeness of God. The most vivid confirmation of this is the 104th psalm of the holy king and prophet David. It poetically narrates about the creation of the world by God and His care about it. Most often, pets are our helpers: they protect us and our property (for example, a dog), make our life easier (for example, a horse), give us food (for example, a cow), and therefore it is natural that we can ask God to give them health in case of sickness. But at the same time, we do not perform special prayers for them at church, during worship, and also we do not comemmorate them.
In the Orthodox Church, the main prayer for people is performed during the Proskomidia, when the priest takes out from the prosphora particles for health or repose of Orthodox Christians. At the end of the Liturgy, these particles are immersed in the Blood of Christ, while the priest asks God to “wash away the sins of those here
commemorated.” Thus, the main essence of prayers is asking God to forgive the sins of a person, whether he is a living member of the Church or the deceased, because sin is the main barrier that separates us from the Creator and does not allow us to connect with Him. Animals, however, never fell away from God, but, according to the holy Apostle Paul, they themselves became victims of the fall of man, as a result of which they “was made subject to vanity and corruption” (see Rom. 8: 20–21).
Even though the Holy Scripture speaks of human immortality and how it will look like, it does not say a word about the eternal life of animals. The modern theologian thinks this way: “Since love is immortal, then love between man and animal is immortal as well. But I have no idea how it all will work.” Therefore, prayer for animals, no matter how close they are to us and no matter how much we love them, is not practiced in the Church.
Source: https://pravlife.org/ru/content/mozhno-li-molitsya-o-zhivotnyh-i-stavit-svechi-za-nih
