An object of the present invention is to provide a filter that makes it possible to suppress the initial pressure loss and, also, to reduce the rising rate of the pressure loss that increases as particulates accumulate; therefore, the pressure loss at the time when a prescribed amount of particulates have been collected becomes lower, and the pressure loss from the viewpoint of the period up to the recovery as a whole also becomes lower. The present invention provides a filter, which is a column shaped filter having a honeycomb structure, including a number of through holes that are placed in parallel with one another in the length direction with wall portion interposed therebetween, wherein the through holes are constituted by two types of through holes, that is, large-capacity through holes having a relatively larger cross-sectional area in the cross section perpendicular to the length direction and small-capacity through holes having a relatively smaller cross-sectional area in the cross section, with the numbers of the two types of through holes being substantially set to the same, the large-capacity through holes are sealed at one end of the filter, while the small-capacity through holes are sealed at the other end of the filter, and supposing that the ratio (a / b) of the total (a) of lengths of wall portion which is shared by one large-capacity through hole and the adjacent large-capacity through hole in the cross section perpendicular to the length direction and the total (b) of lengths of wall portion which is shared by one large-capacity through hole and the adjacent small-capacity through hole in the cross section perpendicular to the length direction is defined as a and that the ratio (A / B) of the area (A) of the cross section of the large-capacity through hole and the area (B) of the cross section of the small-capacity through hole is defined as β, α and β satisfy the relationship represented by the following formula (1): β≧(20 / 9) α2+1 (where 0<α≦1.5 and 1<β≧6) (1).