Initially, Jack and his group viewed the beast as a physical creature to be feared and hunted. However, as the story progresses, their perception of the beast evolves into a symbol of their own inner savagery and fear. They come to see the beast as a means to justify their increasingly violent and chaotic behavior on the island.
Jack's Choir of boys.
Jack's group sacrifices the head of a pig to the beast, placing it on a stick as an offering. This gruesome gesture symbolizes their descent into savagery and their willingness to appease the imagined beast.
The head of a sow on a stick
The pigs head
Ralph and Jack decide to find the beast to prove their leadership and survival skills to the other boys. They believe that by confronting and defeating the beast, they can restore a sense of order and control over the group.
Jack's answer to questions about the beast is to say that, "if there is a beast we will hunt it and kill it." Ralph keeps insisting, "but there is no beast!"
Jack warned his tribe about a number of things. Firstly that if they went hunting they should avoid the mountain and leave the heads of their kills as an offering to the beast. He also warned them to be on their guard as 'the others' (Ralph's group) might try to sneak in, to 'spoil things.' After consideration Jack added that the beast might also try to come in.
Jack and his savages planned to stay on the beast's good side by offering it sacrifices in the form of animal carcasses. They believed that by making these offerings, the beast would be appeased and not harm them. This was a way for them to maintain control and power within their group.
I have read the book recently and I don't think Jack and Ralph believe in the beast. They don't think its actually real, but the idea of the beast existing scares them. Jack even says(to cover his fear) that he and his hunters would find the beast and kill it in Ch.5. So, technically, they are scared but they don't show it as much as the littluns because they are older.
By their adoption of superstitious beliefs and practises such as leaving an offering for the "beast."
In reality, the beast is really the savagery inside the boys, so it changes as they change. However, Jack uses the argument of the beast's deception to keep them afraid and under his control.
they went after the beast but jack decide to forget the beast and play rolling rock