Christians can feel free to cry at a funeral. While we do rejoice that our loved ones who know Christ as Savior go to be with Jesus, death is still a sorrowful time. Jesus did weep at the death of Lazarus (John 11:35). We are not like those without hope (1 Thessalonians 4:13), but as humans, we do feel deeply the absence of a loved one. Maybe we do more because we know God did not create man to die, but to live (Genesis 1-2).
We find the word mourn in 1 Corinthians 5:2. It is the Greek word pentheo. It means, “to mourn, to grieve it is commonly used for mourning for the dead.” This is true in both the Old and New Testaments. It was used by the Old Testament prophets in prophecies of disaster (Joel 1:9, Jeremiah 14:2; Lamentations 2:8) and in the New Testament (Matthew 9:15; Revelation 18:7-8). It is easy to see that mourn communicates an intense sadness and remorse.
The word embodies that inexpressible and profound sense of loss and grief that is experienced when a loved one dies. This level of grief is almost unfathomable because of the unbearable sense of loss and because death is unnatural. God created man to live, but man dies because of sin. Although death is a conquered foe and one day will be done away with completely, for now, all of mankind must die. Man was not created to endure the grief of death. Death is an interloper. The pain of this type of intense loss and grief is only fully understood by someone who also has lost a loved one in death. For them, no communication is necessary for mutual understanding, but the attempt to explain this agony and darkness of the soul to someone who has not lost to death is indeed impossible. The loss of temporal life, the most unnatural of all losses, casts a deep dark shadow over even the brightest of days.
I have preached many funerals over the years, and there is a time during the funeral that I find to be the most intense, nearly an unbearable moment of grief. That is when the guests have been dismissed from the sanctuary, and the family gathers one last time at the side of their departed loved one. As I stand at the head of the casket during this deluge of anguish and emotional upheaval, it is all I can do to remain composed enough to carry out my responsibilities. The summarization of sin and death before them results in uncontrollable crying, wailing, sobbing, moaning, lamenting, crying out to their loved one in affection, and that affection only to be met with coldness, death-chilling coldness. At times, family members have to be pulled away from the casket to which they cling, averse to let go of love and life. Their sobbing is an evocative, haunting, and unnatural cry. It is the cry of death. I know this cry intimately for I have cried it myself.
 Gerhard Kittel, Gerhard Friedrich, and Geoffrey William Bromiley, Theological Dictionary of the New Testament. Translation of: Theologisches Worterbuch Zum Neuen Testament, (Grand Rapids, Mich.: W.B. Eerdmans, 1995, c1985), s.v. “pentheo”.