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Whether the funeral is a religious affair or secular one, it is still appropriate to read bible verses and poems. There is so much comfort to be found in the bible at this time of life, that even people who are not real church goers can appreciate the comfort offered in bible verses. The same holds true with poems. You may not be someone who regularly reads poetry but that does not mean that you would not take comfort in the heartfelt expressions of someone else from a long time ago or just last week.
We all have pain and sorrow when someone dies. These type of feelings have been the same for thousands of years. When you look through history at old funerals you may find that the same bible verses or funeral poems that were read for your loved ones were may have also been used for someone back in history. This is one of the things that connects us to our past. We have all or will all love someone and they will die, that is why when you read a bible passage or verse about death it touches you so deeply because you can relate. It is also very comforting and healing for your soul.
Poems can work the same way. You can search online or in books. Or you may consider writing your feelings down yourself. This can be very therapeutic. When you are done expressing yourself you may consider reading your own poem at the funeral of the loved one you wrote it about.