First of all, I would first like to recommend Monsignor Peter Elliott's excellent guide "Celebrations of the Liturgical Year" published by Ignatius Press in 2002. It is a very useful resource for all those involved in the practical aspects of liturgical planning.
The duration of such veiling varies from place to place. The custom in many places is to veil from before first vespers or the vigil Mass of the Fifth Sunday of Lent while others limit this veiling from after the Mass of the Lord's Supper on Holy Thursday.
In some places images and statues are actually removed from the church and not simply veiled, especially after Holy Thursday.
Crosses are unveiled after the Good Friday ceremonies. All other images are unveiled shortly before the Mass of the Easter Vigil.
Neither the Stations of the Cross nor stained glass windows are ever veiled.
The bishops' conference may decide if the veiling during this period should be obligatory within its territory.
The veils are usually made of lightweight purple cloth without any decoration.
The custom of veiling the images during the last two weeks of Lent hails from the former liturgical calendar in which the Passion was read on the Fifth Sunday of Lent (hence called "Passion Sunday") as well as on Palm Sunday, Tuesday and Wednesday of Holy Week, and Good Friday.
For this reason the period following the Fifth Sunday of Lent was called Passiontide. A remnant of this custom is the obligatory use of the first Preface of the Lord's Passion during the Fifth Week of Lent.
by Fr. Edward McNamara
Professor of liturgy at the Regina Apostolorum Pontifical University.
From EWTN